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<Text-field style="Text" layout="Normal">In this worksheet you will learn how to build a model in MapleSim, and how you can extract the system equations into Maple. Once the equations are extracted, you will use the techniques highlighted in the <Font bold="true">Transient-Response Analysis with Maple </Font>worksheet to analyse the system.</Text-field>
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<Text-field style="Text" layout="Normal">Consider a simple mass-spring-damper system in the figure above. To model this system in MapleSim, drag the following components into the MapleSim environment:</Text-field>
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</Input>
</Group></Presentation-Block></Table-Cell></Table-Row></Table><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L317" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L368" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Step </Font>component into the work area.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Force</Font> into the work area to the right of the Step.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Connect port y of the <Font bold="true">Step </Font>to port f of the Force.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Mass </Font>into the work area to the right of the <Font bold="true">Force</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Connect the flange of Force to <Font italic="true">flange_a </Font>of the <Font bold="true">Mass</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Translational Spring Damper </Font>into the work area to the right of the <Font bold="true">Mass</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Connect <Font italic="true">flange_b </Font>of the <Font bold="true">Inductor </Font>to <Font italic="true">flange_a</Font> of the <Font bold="true">Translational Spring Damper</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Translational Fixed </Font>to the right of the <Font bold="true">Translational Spring Damper</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Connect <Font italic="true">flange_b</Font> of the <Font bold="true">Translational Spring Damper </Font>to the <Font bold="true">Translational Fixed</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Drag a <Font bold="true">Position Sensor </Font>above the <Font bold="true">Mass</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Right-click on the <Font bold="true">Position Sensor </Font>and select <Font bold="true">Rotate Counterclockwise</Font>.</Text-field>
<Text-field style="Text" layout="Normal" bulletsuffix="." initial="-1" bullet="numeric">Connect port <Font italic="true">F</Font> of the <Font bold="true">Position Sensor </Font>to the <Font italic="true">flange_a</Font> of the <Font bold="true">Mass</Font>.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L369" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Once you have completed creating the model as shown above, change the following parameters:</Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L388" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group></Presentation-Block><Table interior="group" showinput="true" alignment="center" exterior="all" width="61.99876619370759%" labelreference="L389" showlabel="true" captionalignment="0" title="" order="row" drawcaption="false" randomized="false" captionposition="1" plotalignlists="" pagebreak="cell" postexecute="insert" showgroup="true"><Table-Column weight="470" separator="true"></Table-Column><Table-Column weight="535" separator="true"></Table-Column><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" fillcolor="[0,51,102]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L390" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" family="Arial" foreground="[255,255,255]" size="14">Component</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell><Table-Cell columnspan="1" backgroundstyle="1" rowspan="1" fillcolor="[0,51,102]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L391" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" family="Arial" foreground="[255,255,255]" size="14">Parameter Change</Font></Text-field>
</Input>
</Group></Presentation-Block></Table-Cell></Table-Row><Table-Row align="top" separator="true"><Table-Cell columnspan="1" backgroundstyle="0" rowspan="1" fillcolor="[255,255,255]"><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L858" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Mass </Text-field>
</Input>
</Group></Presentation-Block><Presentation-Block>
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<Text-field style="Text" layout="Normal">13.	 Drag a box around all components to the right of the step signal.</Text-field>
<Text-field style="Text" layout="Normal">14.	 From the toolbar, go to Edit &gt; Create Subsystem.</Text-field>
<Text-field style="Text" layout="Normal">15.	 Enter <Font italic="true">Mechanical </Font>for the name of the subsystem.</Text-field>
<Text-field style="Text" layout="Normal">16.	 From the model navigation toolbar, select Mechanical from the drop-down menu. This will bring you to the subsystem you just created.</Text-field>
<Text-field style="Text" layout="Normal">17.	 Select the port RO on the <Font bold="true">Position Sensor</Font>. Connect the port to the frame of the subsystem.</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Mass spring damper subsystem</Text-field>
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<Text-field style="Text" layout="Normal">18.	 From the model navigation toolbar, select Main.</Text-field>
<Text-field style="Text" layout="Normal">19. 	Right-click on the port that you just created above on the Mechanical subsystem. Select Attach Probe.</Text-field>
<Text-field style="Text" layout="Normal">20.	 Move the probe to the desired location and click to place the probe.</Text-field>
<Text-field style="Text" layout="Normal">21.	 Press <Image height="28" width="33" zoomable="false" labelreference="L28" drawcaption="false" captionalignment="0" captionposition="1">TUZOV3RLVWI8b2I8Uj1NRExDZE5yRVJES2I7UmN3RVZdXz9eaENfYjtfZHJPdWdJZUVxZ1ZmYk5mYU95a2Nxd3NPbWtoY1xcQWVwTmhGXl5SdmJQT1xcSkZiQ0BeTD5eSlZbbFBiakhiZkFcXFo+XFxZPnI8RnhDXndTQV5rWVpCX19KQFxcVW5oZk5sP0ZsXFxeXkJOWj5AYF5GZGpYdmtheGVQcUVYZE9pdUNIaEpfZnVvZmxuW0RHY19Id2NRd1NIYXFxdW13c3doZD1edVlWdlNObnRAYXFJeHFOd1hHWndpckF3c1NedVBpcWZJaWFXeUd4c3g+YXN4ZztxcXNJc3NZYT14dWdBcD9Aal9OW3BpdkRHXk1PZ3ZvbVlJd0pnZjxBaXBoWlFpcEdpaz5PYz5QZFdhZVV5cFppZUU/YmBRW1l5ZVV3cmlWZ1Vgc1hWW0l4Y29IaG5PbltfY0VgZkhAYVlmb1tWaUB2d1NxYGxgZVxcWXNFeWlaWXRFdmxzV3I9WXFJX2E8eHBRcHZLV3A/TmQ8dmhFX3R2YGJ4eG06WXVfdnNRd2B0QXl3UXNvP3JJPnhzeXNRR3hlYGhbaWA9XnF2ZlxcWmlyaHhzQkBrS2hiWz9eSFl3Sz5hTldlWWlaZG9baGZlVUFyX0BoTz53SD9mV1ZsakdtSWZfRUdmVEhha1Z3c25acnBgPG9bY0ZvQVZkVUZkc09kbVFqPkFsYz5sYF5pT0B5ZGdfQGlyXlZyZmhea1FlcT5yZVZ0R190cmFwUFdeV19lbElwPXhfUmZjZkldWV9eYW9aW2BeZk5qeVlfTEBxPE9nV2dwTF9hcnloQGdcXEQ/dFtfbEhQbEx3YmVJWnJJWz5fYFJfa09ecWBAajt2c1NIY2JgYD9vbF5AaG1gW1dWdT1Xc3A/eF1fXFxbZ3B5SGtDd3NAUV1peXRTYHdtZmBRZltkXmxgQGRESW1pSV5ZXm9bQGpRYWxDWV89TmA9V10/V1psR21bRmRQTmJbV15PbmxbWXk/aGtYbnF4cHFIeGFzcG9tb3FkTmdQQWliV3A/VU9fRFxcc3dPXUVdQ2N2W2JucVk9SVhbW0VHRURDZ2g+TXZMcVZCP2JYeWVIT1dGPVdFc2NPaUlGPXh3dWVZSWhVP0NGQ2JwQ1k7W3VMZWJLW2ZIQ1Q9ZVJbS3RCeVJiaXRKWVhWW3RDW3VdbVVuPXdoQWVLQ0lJRWNHSVc+SUZMeWJkTWNfUWlJc2VlTWNRUVRbdVJnbXJYSVddS2dEW1RfU1d4VUN2TUVdc0M9PVN0dUlEZUZwQ2luR0JVV3Q7PWdVQWNGRUZgY2lMbXNPQUk7eWhxS1lyP3VJX1NMU3d0SWZwPUdfV2J1bXVqYWVMQ1NIdURDV1dPX2lhc3ZDa0lHU0ZuSVVkdXRkbUh1O2NUW0U8U2hzb2djW3ZjUVNGTXV2cURjW1lBeXNpR0hcXENCPUFYOkd0Uld2bmdTSF1jVGVXRnd2Z1F0QlNpSndTZ19JXm9TYFFJQj9HS09SPjtEZltWUG9nQ0tHYFlmTGN4VnV0cGN1QD1DdmFoU3lySVtleENpeW1YXFxHVzpZSTxddUtvST1LYmlTZ05Pc2lNU19bQmFtVlVIUl5FdGBUTUxgbUlIT1NoUUVZVkF1VG1cXHFwZFBHcFJ1YU5ycHM/ZFNTQG1xaVFUVExgVVFlZU5AWFJVZFFnUFRnXVhOXFxWc1lwdExLUHVNRFV3c2RZWERtdkR4WlxcVVFMbGdYUml0dD9ka29EamlYT0d1S2Vkdzpod0BYaj1xWUdhWVZNb0tIalFkVlU9VF9cXG91eVdqcWxNXW9fRGBUSHZRYWpLSWpcXGZbTj9kPV9idGZqXkl5PlZkXk90a0hoXFxYdFxcV1tLcWpJV2JNbnQ9RmY6WW9LT2l4UGRWYHFaWWFVQ3BFd2tZZW5LRD9HQj5jZGtRSExRVz09WGdRaUVvZlFXdnJVdEBZeFdvSEh1aGVhZ0JxaHNdVXlVV3RXQj9JRTxFZGRjQ2pLU21nUmlZR09LZ0xPVV1PVm9nc2M/SWhVRjpZQ2d1REltaFI9ZjxTQ2FPVUdbWFNDY1VbVFVXaVVdZmhVV2tTeFVNZFNNSEVXaVBreUxXY2hDWWdhWFU7SXBDdTpZVW1jU1ZPV3RbV1lbZEtxeFhzZVNpV3l3d0ZjQ3JlUlljZ1VrRGFPaEVHU3Q/RlE7WVpHdltpeV1zQmpdV2BNQ0dNWHZlZltBZUBjc0NZY0dPQz9nWFFpY1NBZDp5V1tPY1t3Qkc/d2c9Um5LRXJTaHJzYlNvU0FTaF5heFVTQ01BVWZxSG9xU1dBWVR1RF9DaHdheGVxZzx3RE9xVj5tRFZzdFVrVERRYz15eGFrRj1bWXJdeWprU3hbSEU/SUM9dFxcd3JdQUlvW0dMeWNHS2lfW0VcXHVUY1dVPFNzYlNDVl9CYXVkUEN4WEl3TT9ZcG15Wlt5QGNYVUlEUmFTbVNYbktGQF9oS2dYQFtWc0NySmljd0F1Xkt3VlFyRmtkYXdmWlVoVG9peE1WQ3N2UHdjSllzRFN3VUN2Z2V5VkFlcTt2P29DcU9iOmtZdWdXSmVpdE9oPndYWE9JSE9FTUNoYFdZVGtXRF12QnNzaG14RmtVPVN0Z1d3RXVjWGtyWz9ycWNVX0llP0lZdltZak11UktkPkVIPGFocm1SQkd0VlNJZ0lFdk1kT1NlYXlmYXlDW1RLbW12WHB3SXlXblF5VVF1eEl0V1xceXNUakVgbmx0SmZoUlhxTE5EdXF5Vk9oTHJgbEs8dG15cVBxUndseVl1WWhcXFd5PHJZeXNdcW1wYXl3SVBoSGhYeV5SUHdgWW5oWGY6SjpgblxcdE5cXHRUWzxQOzszOlwiXHtcfQ==<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkSSRGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiQhR0YqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image>  to run the simulation.</Text-field>
<Text-field style="Text" layout="Normal">22.	 Save your model.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Simulation output</Text-field>
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<Text-field style="Heading 1" layout="Heading 1">State Space Representations</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Consider the mechanical system above. The displacement <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEieUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==</Equation> is measured from equilibrium in the absence of an external force <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYsNiVRInRGJ0YvRjIvRjNRJ25vcm1hbEYnRj1GPQ==</Equation>. This system is a single-input single-output system.</Text-field>
<Text-field style="Text" layout="Normal">For this system, we know that </Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">This system is of second order. This means that the system involves two integrators. Define two state variables <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInRGJ0YyRjVGPkY+Rj4=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInRGJ0YyRjVGPkY+Rj4=</Equation> and <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ0RidGMkY1Rj5GPkY+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYkLUkjbW5HRiQ2JFEiMkYnL0Y2USdub3JtYWxGJ0Y+LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GLzYlUSJ0RidGMkY1Rj5GPkY+</Equation> as</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMUYnL0Y2USdub3JtYWxGJ0YyRjUvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYvNiVRInRGJ0YyRjVGPkY+LUkjbW9HRiQ2LVEiPUYnRj4vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRlEvJSlzdHJldGNoeUdGUS8lKnN5bW1ldHJpY0dGUS8lKGxhcmdlb3BHRlEvJS5tb3ZhYmxlbGltaXRzR0ZRLyUnYWNjZW50R0ZRLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGam4tRi82JVEieUYnRjJGNUZDRj4=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Then we obtain</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">or rearranging the second equation,</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21vR0YkNi1RIi5GJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVEY1RjgvRlFGNy1GIzYlLUkjbW5HRiQ2JFEiMUYnRkFGNUY4LyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSShtZmVuY2VkR0YkNiQtRiM2JC1GMjYlUSJ0RidGNUY4RkFGQS1GPjYtUSI9RidGQUZDRkZGSEZKRkxGTkZQL0ZTUSwwLjI3Nzc3NzhlbUYnL0ZWRmdvLUYsNiVGMS1GIzYlLUZlbjYkUSIyRidGQUY1RjhGaG5GW29GQQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21vR0YkNi1RIi5GJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVEZBL0ZRRjctRiM2JC1JI21uR0YkNiRRIjJGJ0ZBRkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYyNiVRInRGJ0Y1RjhGQUZBLUY+Ni1RIj1GJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGZ28tRj42LVEifkYnRkFGQ0ZGRkhGSkZMRk5GUEZSRlUtSSZtZnJhY0dGJDYoLUYyNiVRImNGJ0Y1RjgtRiM2JS1GMjYlUSJtRidGNUY4RjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHEvJSliZXZlbGxlZEdGRS1GLDYlRjEtRiM2JS1GZW42JEZpcEZBRjVGOEZobkZbb0Zpby1GPjYtUSomdW1pbnVzMDtGJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGW3JGaW8tRl1wNigtRjI2JVEiZEYnRjVGOEZicEZncEZqcEZdcUZfcUZpby1GLDYlRjEtRiM2JUZaRjVGOEZobkZbby1GPjYtUSIrRidGQUZDRkZGSEZKRkxGTkZQRmpxRlxyLUZdcDYoRmVxRmJwRmdwRmpwRl1xRl9xLUYyNiVRImZGJ0Y1RjhGQQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY0LUklbXN1YkdGJDYlLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRInhGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JC1JI21vR0YkNi1RIi5GJy9GOVEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGVEZBL0ZRRjctRiM2JC1JI21uR0YkNiRRIjJGJ0ZBRkEvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1JKG1mZW5jZWRHRiQ2JC1GIzYkLUYyNiVRInRGJ0Y1RjhGQUZBLUY+Ni1RIj1GJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjc3Nzc3OGVtRicvRlZGZ28tRj42LVEifkYnRkFGQ0ZGRkhGSkZMRk5GUEZSRlUtSSZtZnJhY0dGJDYoLUYyNiVRImNGJ0Y1RjgtRiM2JS1GMjYlUSJtRidGNUY4RjVGOC8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXHEvJSliZXZlbGxlZEdGRS1GLDYlRjEtRiM2JS1GZW42JEZpcEZBRjVGOEZobkZbb0Zpby1GPjYtUSomdW1pbnVzMDtGJ0ZBRkNGRkZIRkpGTEZORlAvRlNRLDAuMjIyMjIyMmVtRicvRlZGW3JGaW8tRl1wNigtRjI2JVEiZEYnRjVGOEZicEZncEZqcEZdcUZfcUZpby1GLDYlRjEtRiM2JUZaRjVGOEZobkZbby1GPjYtUSIrRidGQUZDRkZGSEZKRkxGTkZQRmpxRlxyLUZdcDYoRmVxRmJwRmdwRmpwRl1xRl9xLUYyNiVRImZGJ0Y1RjhGQQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">We can rewrite the above in vector-matrix form,</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" 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<Text-field style="Heading 1" layout="Heading 1">Extracting the Equation from a MapleSim Model</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">Working with model created above, go to the attachments folder by clicking on the paperclip <Image height="23" width="21" zoomable="false" labelreference="L32" drawcaption="false" captionalignment="0" captionposition="1">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkNSNGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRJI0YqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image>   located in the top toolbar. From here, load the Equations template. This will load the template in Mpale. From this template you will be able to extract the equations for your model and can manipulate them in various ways.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Step 1: Subsystem Selection</Font></Text-field>
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<Text-field style="Text" layout="Normal">1.  In the model diagram, select the subsystem Mechanical from the model navigation toolbar.<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">2.  Press &quot;Load Selected Subssytem.&quot;</Text-field>
<Text-field style="Text" layout="Normal">3.	  Scroll down to Parameter and Variable Manipulation. In the Parameters table, change the following parameter names values (note that the 1 used in the parameter names may be different values in your model):</Text-field>
<Text-field style="Text" layout="Normal">         a.  <Font italic="true">Main.mechanical1.M1.m </Font>    m</Text-field>
<Text-field style="Text" layout="Normal">         b.	  <Font italic="true">Main.mechanical1.SD1.c</Font>      c</Text-field>
<Text-field style="Text" layout="Normal">         c.  	<Font italic="true">Main.mechanical1.SD1.d	 </Font>     d</Text-field>
<Text-field style="Text" layout="Normal">3.	  In the Symbolic column, place an X next to each of these names</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Parameter manager</Text-field>
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<Text-field style="Text" layout="Normal">4.	  Press Reassign Equations.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Step 2: View and Manipulate Equations</Font></Text-field>
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<Text-field style="Text" layout="Normal">5. The DAE's should appear in the equation window. You can view all equation types by selecting the radio button that corresponds to the equation type.</Text-field>
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<Text-field style="Text" layout="Normal">6.	  Move the mouse cursor to the blank workspace below the template.</Text-field>
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<Text-field style="Text" layout="Normal">7.  Insert a new document block by going to Format &gt; Create New Document Block.</Text-field>
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<Text-field style="Text" layout="Normal">8.  Enter <Font italic="true">with(DynamicSystems)</Font>. This will load the Dynamic Systems package.</Text-field>
<Text-field style="Text" layout="Normal">9.	  Assign the equations to a variable by entering <Font italic="true">myeqs:=DAEs</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Step 3: Creating State Space Equations</Font></Text-field>
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<Text-field style="Text" layout="Normal">10.	  Right-click on the system equations and go to DynamicSystems &gt; Conversions &gt; Differential Equations to State Space.</Text-field>
<Text-field style="Text" layout="Normal">11.  	For the system input, select <Font italic="true">RI1(t)</Font>. For the system output, select <Font italic="true">SD1_s_rel(t)</Font>.</Text-field>
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<Text-field style="Text" layout="Normal">12.	The state space matrices A, B, C and D will be displayed.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Using Maple commands</Font></Text-field>
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<Text-field style="Text" layout="Normal">13.	 Enter the following commands into Maple:</Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      input:=RI1(t)</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      output:=</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEqU0QxX3NfcmVsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRjEvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0YzUSdub3JtYWxGJ0ZCRj1GP0ZC">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEqU0QxX3NfcmVsRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEidEYnRi9GMi8lK2V4ZWN1dGFibGVHRjEvJTBmb250X3N0eWxlX25hbWVHUSkyRH5JbnB1dEYnL0YzUSdub3JtYWxGJ0ZCRj1GP0ZC</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      mysys:=StateSpace(myeqs, input , output):</Font></Text-field>
<Text-field style="Text" layout="Normal">14.	 To view the system object, type <Font italic="true">PrintSystem(mysys)</Font> </Text-field>
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<Text-field style="Text" layout="Normal">You can extract the individual state space matrices and assign them to variable names for use later. We will use these extract matrices in the next example.</Text-field>
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<Text-field style="Text" layout="Normal">15.  Enter <Font italic="true">AA:=mysys:-a</Font> to extract the state matrix and assign it to <Font italic="true">AA</Font>.</Text-field>
<Text-field style="Text" layout="Normal">16.  Enter <Font italic="true">BB:=mysys:-b</Font> to extract the state matrix and assign it to <Font italic="true">BB</Font>.</Text-field>
<Text-field style="Text" layout="Normal">17.  Enter <Font italic="true">CC:=mysys:-c</Font> to extract the state matrix and assign it to <Font italic="true">CC</Font>.</Text-field>
<Text-field style="Text" layout="Normal">18.  Enter <Font italic="true">DD:=mysys:-d</Font> to extract the state matrix and assign it to <Font italic="true">DD</Font>. (Note that you cannot use the name <Font italic="true">D</Font> as it is a protected name in Maple)</Text-field>
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</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 1" layout="Heading 1">Obtaining Transfer Functions</Text-field></Title>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Conversions from statespace to transfer functions</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">Consider again the mechanical system shown above. Using the state-space equations calculated for the system, we shall obtain the transfer functions for the system.</Text-field>
<Text-field style="Text" layout="Normal">Using the fundamental relationship,</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">we can obtain,</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 3" layout="Heading 3">Verifying the relationship using Maple</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">Recall from the previous derivation <Equation executable="false" style="2D Math" input-equation="" 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,  <Equation executable="false" style="2D Math" input-equation="" 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, <Equation executable="false" style="2D Math" input-equation="" 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<Text-field style="Text" layout="Normal">The following are a series of Maple commands verifying the conversion between the statespace and transfer function representations. Note that double letter variables are used to minimize the chance of conflict with protected variable names such as <Font italic="true">D </Font>and <Font italic="true">I</Font>.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L546" drawlabel="true" redirect-source="L513">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L513" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNT1oejYtM1duVz0=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L514" drawlabel="true" redirect-target="L547">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L547" drawlabel="true" redirect-source="L514">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L514" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSdjb2x1bW5HRig2Iy9JJCVpZEdGKCI1bVZeOC0zV25XPQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L515" drawlabel="true" redirect-target="L548">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L548" drawlabel="true" redirect-source="L515">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L515" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSRyb3dHRig2Iy9JJCVpZEdGKCI1LXBgOC0zV25XPQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L878" drawlabel="true" redirect-target="L879">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L879" drawlabel="true" redirect-source="L878">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L878" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIh</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L537" drawlabel="true" redirect-target="L549">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L549" drawlabel="true" redirect-source="L537">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L537" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUkobWFjdGlvbkc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYoLUklbXJvd0dGJDYmLUknbXRhYmxlR0YkNjYtSSRtdHJHRiQ2Jy1JJG10ZEdGJDYoLUkjbW5HRiQ2JFEiMUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGQy8lK2dyb3VwYWxpZ25HRkMvJShyb3dzcGFuR0Y9LyUrY29sdW1uc3BhbkdGPS1GODYoLUY7NiRRIjBGJ0Y+RkFGREZGRkhGSkZBRkRGRi1GNTYnRkxGN0ZBRkRGRi8lJmFsaWduR1ElYXhpc0YnL0ZCUSliYXNlbGluZUYnL0ZFUSZyaWdodEYnL0ZHUSd8ZnJsZWZ0fGhyRicvJS9hbGlnbm1lbnRzY29wZUdRJXRydWVGJy8lLGNvbHVtbndpZHRoR1ElYXV0b0YnLyUmd2lkdGhHRltvLyUrcm93c3BhY2luZ0dRJjEuMGV4RicvJS5jb2x1bW5zcGFjaW5nR1EmMC44ZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRmZvLyUmZnJhbWVHRmZvLyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dRJmZhbHNlRicvJS1lcXVhbGNvbHVtbnNHRmBwLyUtZGlzcGxheXN0eWxlR0ZgcC8lJXNpZGVHRlkvJTBtaW5sYWJlbHNwYWNpbmdHRmNvLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0ZgcEY+Rj4vSSttc2VtYW50aWNzR0YkUSdNYXRyaXhGJy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZecS8lK2FjdGlvbnR5cGVHUS5ydGFibGVhZGRyZXNzRicvJSlydGFibGVpZEdRNTE4NDQ2NzQ0MDgwMjExNzk2NzI2Ric=">LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNUVuejYtM1duVz0=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L538" drawlabel="true" redirect-target="L550">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L550" drawlabel="true" redirect-source="L538">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L538" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNXlvejYtM1duVz0=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L539" drawlabel="true" redirect-target="L551">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L551" drawlabel="true" redirect-source="L539">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L539" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknTWF0cml4RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMvSSQlaWRHRiciNUlxejYtM1duVz0=</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L540" drawlabel="true" redirect-target="L552">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
</Input>
<Output>
<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="centred" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"><Equation executable="false" style="2D Output" display="LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=">LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=</Equation></Text-field>
</Output>
</Group>
<Group view="presentation" hide-input="true" hide-output="false" inline-output="false" labelreference="L552" drawlabel="true" redirect-source="L540">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L540" view="label" executable="true"></Label>); # input placeholder</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSZJJ1ZlY3Rvckc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjSSRyb3dHRig2Iy9JJCVpZEdGKCI1dXJgOC0zV25XPQ==</Equation></Text-field>
</Output>
</Group></Presentation-Block><Presentation-Block>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1JJW1zdXBHRiQ2JS1JKG1mZW5jZWRHRiQ2JC1GIzYpLUYsNiVRInNGJ0YvRjJGNS1GLDYlUSNJREYnRi9GMi1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORltvRjUtRiw2JVEiQUYnRi9GMkY5RjktRiM2JS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGam5GXG8tSSNtbkdGJDYkUSIxRidGOUY5LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJ0Y1LUYsNiVRIkJGJ0YvRjItRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZqbkZcby1GLDYlUSNEREYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOQ==</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">print(<Label label="L541" view="label" executable="true"></Label>); # input placeholder</Text-field>
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<Text-field style="Text" layout="Normal">Although the expression is written slightly differently, it is clear that this is entirely equivalent to <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2LS1JI21pR0YkNiVRIm1GJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRictSSNtb0dGJDYtUSJ+RidGMi8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGRi8lKXN0cmV0Y2h5R0ZGLyUqc3ltbWV0cmljR0ZGLyUobGFyZ2VvcEdGRi8lLm1vdmFibGVsaW1pdHNHRkYvJSdhY2NlbnRHRkYvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZVLUklbXN1cEdGJDYlLUY4NiVRInNGJ0Y7Rj4tRiM2JC1GLzYkUSIyRidGMkYyLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy1GQTYtUSIrRidGMkZERkdGSUZLRk1GT0ZRL0ZUUSwwLjIyMjIyMjJlbUYnL0ZXRmRvLUY4NiVRImRGJ0Y7Rj5GQEZlbkZARmBvLUY4NiVRImNGJ0Y7Rj5GMi8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYHAvJSliZXZlbGxlZEdGRkYy</Equation></Text-field>
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<Text-field style="Text" layout="Normal">This example also shows how you can very quickly convert statespace models to transfer function equivalents. Simply enter the final formula taking care that your original matrices are defined appropriately.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Using context sensitive menus</Font></Text-field>
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<Text-field style="Text" layout="Normal">Another way is to use the context sensitive menus which recognizes models defined through the <Font italic="true">DynamicSystems</Font> library. For example,</Text-field>
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<Text-field style="Text" layout="Normal">1.  Recall the system equations by entering <Font italic="true">myeqs</Font>.</Text-field>
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<Text-field style="Text" layout="Normal">2.  Right-click on the system equations and go to DynamicSystems &gt; Conversions &gt; Differential Equations to Transfer Functions.</Text-field>
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<Text-field style="Text" layout="Normal">3.  For the system input, select <Font italic="true">RI1(t)</Font>. For the system output, select <Font italic="true">SD1_s_rel(t)</Font>.</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Heading 1" layout="Heading 1">Time Response Information from Models</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">For this example, recall the model built for the previous section <Font italic="true">Extracting the statespace equation from a MapleSim model</Font>. For that model, we assigned the name <Font italic="true">mysys</Font> to the statespace representation of the system using the <Font italic="true">DynamicSystems</Font> function <Font italic="true">StateSpace</Font>. </Text-field>
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<Text-field style="Text" layout="Normal">To obtain a step response in time, we first, we need to assign parameter values to the model. Assume the following values for the parameters and assign them to Maple variables</Text-field>
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<Text-field style="Text" layout="Normal">To generate the response plot, enter the command and refer to <Font italic="true">mysys</Font>.</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Unit-step response of the mass spring damper</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">To get more precise information about the response, we can use the StepProperties command to calculate rise time, peak time, maximum overshoot, and settling time. Continuing with the example from above, enter the command</Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRL1N0ZXBQcm9wZXJ0aWVzRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEmbXlzeXNGJ0YvRjJGOUY5Rjk=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUYsNiVRL1N0ZXBQcm9wZXJ0aWVzRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEmbXlzeXNGJ0YvRjJGOUY5Rjk=</Equation></Text-field>
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<Text-field style="Text" layout="Normal">Extract the unit-step properties and assign them to the variable<Font family="Arial" size="10"> </Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation>. The command will return a sequence of ordered pairs of key time response characteristics in the following order. For the list of properties, see the <Hyperlink linktarget="Help:StepProperties" hyperlink="true"><Font style="Text" underline="true" foreground="[0,128,128]">StepProperties</Font></Hyperlink> help page.</Text-field>
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<Text-field style="Text" layout="Normal">Using these values one can easily calculate the rise time, peak time, maximum overshoot and settling time using the following commands (note this assumes we use the variable <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation> to catch the results of the <Font italic="true">SetProperties </Font><Font encoding="UTF-8">command)\302\270</Font></Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Rise time: <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>   </Text-field>
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<Text-field style="Text" layout="Normal" bullet="dot">Peak time:	<Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Maximum overshoot:	 <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Settling time:	 <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUkjbW5HRiQ2JFEiN0YnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjFGJ0Y+Rj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JVElcHJvcEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2Ji1GIzYmLUkjbW5HRiQ2JFEiN0YnL0YzUSdub3JtYWxGJy1JI21vR0YkNi1RIixGJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0YxLyUpc3RyZXRjaHlHRkYvJSpzeW1tZXRyaWNHRkYvJShsYXJnZW9wR0ZGLyUubW92YWJsZWxpbWl0c0dGRi8lJ2FjY2VudEdGRi8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHUSwwLjMzMzMzMzNlbUYnLUY7NiRRIjFGJ0Y+Rj5GPi8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Y+</Equation></Text-field>
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<Text-field style="Text" layout="Normal">For the mass spring damper example, these values are</Text-field>
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<Text-field style="Text" layout="Normal" bullet="dot">Rise time: 	1.51582015529032</Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Peak time:	 3.99183918248875</Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Maximum overshoot:	 0.0382534619504988</Text-field>
<Text-field style="Text" layout="Normal" bullet="dot">Settling time:	 21.0911517405657</Text-field>
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<Text-field style="Text" layout="Normal">The output format of the <Font italic="true">StepProperties</Font> function is a Maple sequence and this provides a convenient way to visualize the time response properties. For example, we can use an extension of the standard Maple <Font italic="true">plot</Font> command to combine the basic time response plot with markers for the various properties just calculated. For example, in this case, </Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">It is often very convenient to obtain an electrical equivalent circuit analogous to a mechanical system. We can then apply Kirchhoff\342\200\231s laws to write the circuit equations and determine the transfer function. It is also possible to write these equations directly in terms of the Laplace transforms of the currents and voltages. Furthermore, one can use network theorems to simplify the circuits. Electrical analogs for mechanical systems have also been used for simulations. In particular, if one uses the force-current/force-torque analogy, the topology of the electrical analog is very similar to that of the mechanical system.</Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Font bold="true" family="Arial" foreground="[255,255,255]" size="14">Mechanical (rotational)</Font></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Current, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiaUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Force, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Torque, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiVEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Voltage, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Velocity, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Angular velocity, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5Njk7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Flux linkages, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUScmIzk2NjtGJy9GMEY9RjlGOQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVEiTkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUScmIzk2NjtGJy9GMEY9RjlGOQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Displacement, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEieEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Angular displacement, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NTI7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy</Equation></Text-field>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L662" drawlabel="true">
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<Text-field style="Text" layout="Normal" alignment="centred">Capacitance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiQ0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Mass, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Moment of intertia, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiSkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Conductance, <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Damping coefficient, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Rotational damping coefficient, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiREYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal" alignment="centred">Inductance, <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEiTEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic=</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Compliance, <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> of spring</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Torsional compliance, <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation> of spring</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"> <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJERidGL0YyLUY2Ni5RIn5GJ0YvRjJGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRInZGJ0YvRjJGOQ==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUSJERidGL0YyLUY2Ni5RIn5GJ0YvRjJGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZWLUYsNiVRInZGJ0YvRjJGOQ==</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"> <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal">For example the electrical analog of a mass on wheels, connected by a spring to a rigid body is shown below</Text-field>
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<Text-field style="Text" layout="Normal">It can be shown that both the mechanical system and its electrical equivalent circuit have two nodes, the ground and the node corresponding do the displacement x, or the voltage v. The differential equation for both systems is given as</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">In the case of the electrical network, the equation was obtained by applying Kirchhoff\342\200\231s current law at the node v, and is identical to the equation that would have been obtained by applying D\342\200\231Alembert\342\200\231s principle to the mechanical system.</Font></Text-field>
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<Text-field style="Text" layout="Normal">Taking the Laplace transforms of both sides of the equation, assuming zero initial conditions, we get the transfer function</Text-field>
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<Text-field style="Heading 2" layout="Heading 2">Building the electrical system in MapleSim</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal">To construct the equivalent mechanical and electrical models in MapleSim:</Text-field>
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<Text-field style="Text" layout="Normal">Note that an integrator component is required in the electrical circuit since <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation>.</Text-field>
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<Text-field style="Text" layout="Normal">We have already built the mechanical model and have generated the transfer function for the model. To build the electrical equivalent, drag the following components into a new MapleSim session</Text-field>
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<Text-field style="Text" layout="Normal">Select all of the components except for the <Font bold="true">Step Signal </Font>and collapse everything into a subsystem. Name the subsystem <Font italic="true">Electrical</Font>. Navigate down into the subsystem and connect the <Font bold="true">Voltage Sensor </Font>to the frame. Navigate to the top level of the model and attach a probe to the port just created. Run the simulation. The output for the simulation is the same as for the spring-mass-damper.</Text-field>
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<Text-field style="Text" layout="Normal">Working with the model created above, go to the attachments folder by clicking on the paperclip <Image height="23" width="21" zoomable="false" labelreference="L32" drawcaption="false" captionalignment="0" captionposition="1">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<Drawing-Root>LSUlUk9PVEc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZR0YnLSUtQk9VTkRTX1dJRFRIRzYjJCIkNSNGKi0lLkJPVU5EU19IRUlHSFRHNiMkIiRJI0YqLSUpQ0hJTERSRU5HNiI=</Drawing-Root></Image>   located in the top toolbar. From here, load the Equations template. This will load the template in Mpale. From this template you will be able to extract the equations for your model and can manipulate them in various ways.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Step 1: Subsystem Selection</Font></Text-field>
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<Text-field style="Text" layout="Normal">1.  In the model diagram, select the subsystem electrical from the model navigation toolbar.<Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal">2.  Press &quot;Load Selected Subssytem.&quot;</Text-field>
<Text-field style="Text" layout="Normal">3.	  Scroll down to Parameter and Variable Manipulation. In the Parameters table, change the following parameter names values (note that the 1 used in the parameter names may be different values in your model):</Text-field>
<Text-field style="Text" layout="Normal">         a.  <Font italic="true">Main.electrical.C1.C </Font>    m</Text-field>
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<Text-field style="Text" layout="Normal">         c.  	<Font italic="true">Main.electrical1.I1.L		  </Font>     <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21pR0YkNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGO0Y+LyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjI=">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiRRIjFGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21pR0YkNiVRImRGJy8lJ2l0YWxpY0dRJXRydWVGJy9GM1EnaXRhbGljRidGO0Y+LyUubGluZXRoaWNrbmVzc0dGMS8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZELyUpYmV2ZWxsZWRHUSZmYWxzZUYnRjI=</Equation></Text-field>
<Text-field style="Text" layout="Normal">3.	  In the Symbolic column, place an X next to each of these names</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Parameter manager</Text-field>
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<Text-field style="Text" layout="Normal">4.	  Press Reassign Equations.</Text-field>
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<Text-field style="Text" layout="Normal">5.	  Move the mouse cursor to the blank workspace below the template.</Text-field>
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<Text-field style="Text" layout="Normal">6.  Insert a new document block by going to Format &gt; Create New Document Block.</Text-field>
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<Text-field style="Text" layout="Normal">7.  Enter <Font italic="true">with(DynamicSystems)</Font>. This will load the Dynamic Systems package.</Text-field>
<Text-field style="Text" layout="Normal">8.	  Assign the equations to a variable by entering <Font italic="true">myeqs:=DAEs</Font></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field style="Text" layout="Normal">10.	  Right-click on the system equations and go to DynamicSystems &gt; Conversions &gt; Differential Equations to Transfer Function.</Text-field>
<Text-field style="Text" layout="Normal">11.  	For the system input, select <Font italic="true">RI1(t)</Font>. For the system output, select <Font italic="true">I2_y(t)</Font>.</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">Input/output selection</Text-field>
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<Text-field style="Text" layout="Normal">12.	The transfer function will be displayed.</Text-field>
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<Text-field style="Text" layout="Normal"><Font bold="true">Using Maple commands</Font></Text-field>
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<Text-field style="Text" layout="Normal">13.	 Enter the following commands into Maple:</Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      input:=RI1(t)</Font></Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      output:=</Font><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElSTJfeUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0YxLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GM1Enbm9ybWFsRidGQkY9Rj9GQg==">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVElSTJfeUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYmLUYsNiVRInRGJ0YvRjIvJStleGVjdXRhYmxlR0YxLyUwZm9udF9zdHlsZV9uYW1lR1EpMkR+SW5wdXRGJy9GM1Enbm9ybWFsRidGQkY9Rj9GQg==</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Font italic="true">      mysys:=TransferFunction(myeqs, input , output):</Font></Text-field>
<Text-field style="Text" layout="Normal">14.	 To view the system object, type <Font italic="true">PrintSystem(mysys)</Font> </Text-field>
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