<?xml version="1.0" encoding="UTF-8"?>
<project id="r1" sign="nSet" labelFontsize="18" arrowFontsize="12" name="Mathematical pendulum" boxFontsize="12" maxTree="-1" version="7.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="file:/de/consideo/resources/dtd/project.xsd">
  <description id="r2" compareStartTime="NaN" compareTimeUnit="months" compareEndTime="NaN" compareStartDate="">
    <boundary id="r3" name="--empty--"/>
    <objective id="r4" name="-- empty --"/>
    <problem id="r5" name="-- empty --"/>
  </description>
  <discussion id="r6">
    <relation id="r7" to="r8" from="r9" type="annotate"/>
    <statement id="r8" author="borneman" subject="unbenannt" date="1073307265403" type="annotation"/>
  </discussion>
  <exchange id="r10"/>
  <exploration id="r11">
    <diagram id="r12" ref="r13" exploreBoxWidth="100" exploreBoxHeight="55" type="brainstorming" bgDiagramName=""/>
    <draft id="r13" name=""/>
    <exchange id="r14"/>
  </exploration>
  <scenarios id="r15" defaultScenario="r16">
    <scenario id="r16" author="" subject="" simcockpits="r17" name="default" date="0">
      <curve id="r18" includeZero="true" minValue="0" frozen="false" ref="r19" style="default" color="0 0 255" autoRange="true" maxValue="0"/>
      <curve id="r20" includeZero="true" minValue="0" frozen="false" ref="r21" style="default" color="255 0 255" autoRange="true" maxValue="0"/>
      <curve id="r22" includeZero="true" minValue="0" frozen="false" ref="r23" style="default" color="128 128 128" autoRange="true" maxValue="0"/>
      <curve id="r24" includeZero="true" minValue="0" frozen="false" ref="r25" style="default" color="0 0 178" autoRange="true" maxValue="0"/>
      <curve id="r26" includeZero="true" minValue="0" frozen="false" ref="r27" style="default" color="178 0 0" autoRange="true" maxValue="0"/>
      <curve id="r28" includeZero="true" minValue="0" frozen="false" ref="r29" style="default" color="0 178 0" autoRange="true" maxValue="0"/>
      <curve id="r30" includeZero="true" minValue="0" frozen="false" ref="r31" style="default" color="178 140 0" autoRange="true" maxValue="0"/>
      <curve id="r32" includeZero="true" minValue="0" frozen="false" ref="r33" style="default" color="178 0 178" autoRange="true" maxValue="0"/>
      <curve id="r34" includeZero="true" minValue="0" frozen="false" ref="r35" style="default" color="0 0 0" autoRange="true" maxValue="0"/>
      <curve id="r36" includeZero="true" minValue="0" frozen="false" ref="r37" style="default" color="0 0 255" autoRange="true" maxValue="0"/>
      <curve id="r38" includeZero="true" minValue="0" frozen="false" ref="r39" style="default" color="255 0 255" autoRange="true" maxValue="0"/>
      <curve id="r40" includeZero="true" minValue="0" frozen="false" ref="r41" style="default" color="128 128 128" autoRange="true" maxValue="0"/>
      <curve id="r42" includeZero="true" minValue="0" frozen="false" ref="r43" style="default" color="0 0 178" autoRange="true" maxValue="0"/>
      <curve id="r44" includeZero="true" minValue="0" frozen="false" ref="r45" style="default" color="178 0 0" autoRange="true" maxValue="0"/>
      <curve id="r46" includeZero="true" minValue="0" frozen="false" ref="r47" style="default" color="0 178 0" autoRange="true" maxValue="0"/>
      <curve id="r48" includeZero="true" minValue="0" frozen="false" ref="r49" style="default" color="178 140 0" autoRange="true" maxValue="0"/>
      <curve id="r50" includeZero="true" minValue="0" frozen="false" ref="r51" style="default" color="178 0 178" autoRange="true" maxValue="0"/>
      <curve id="r52" includeZero="true" minValue="0" frozen="false" ref="r53" style="default" color="0 0 0" autoRange="true" maxValue="0"/>
      <curve id="r54" includeZero="true" minValue="0" frozen="false" ref="r55" style="default" color="0 0 255" autoRange="true" maxValue="0"/>
      <curve id="r56" includeZero="true" minValue="0" frozen="false" ref="r57" style="default" color="255 0 255" autoRange="true" maxValue="0"/>
      <curve id="r58" includeZero="true" minValue="0" frozen="false" ref="r59" style="default" color="128 128 128" autoRange="true" maxValue="0"/>
      <curve id="r60" includeZero="true" minValue="0" frozen="false" ref="r61" style="default" color="0 0 178" autoRange="true" maxValue="0"/>
      <diagram id="r62" ref="r63" exploreBoxWidth="100" exploreBoxHeight="55" type="cld" bgDiagramName="">
        <arrow id="r64" to="r65" navcoords="" colorstyle="color=-12566464 " from="r66" ylabel="-1" fromPortNo="0" ref="r67" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r68" xpos="431" ypos="458"/>
          <coord id="r69" xpos="389" ypos="450"/>
          <coord id="r70" xpos="251" ypos="360"/>
        </arrow>
        <arrow id="r71" to="r72" navcoords="" colorstyle="color=-12566464 " from="r65" ylabel="-1" fromPortNo="0" ref="r73" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r74" xpos="264" ypos="333"/>
          <coord id="r75" xpos="403" ypos="336"/>
          <coord id="r76" xpos="529" ypos="320"/>
        </arrow>
        <arrow id="r77" to="r78" navcoords="" colorstyle="color=-12566464 " from="r72" ylabel="-1" fromPortNo="0" ref="r79" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r80" xpos="529" ypos="293"/>
          <coord id="r81" xpos="427" ypos="256"/>
          <coord id="r82" xpos="249" ypos="143"/>
        </arrow>
        <arrow id="r83" to="r84" navcoords="" colorstyle="color=-12566464 " from="r78" ylabel="-1" fromPortNo="0" ref="r85" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r86" xpos="261" ypos="99"/>
          <coord id="r87" xpos="408" ypos="55"/>
          <coord id="r88" xpos="515" ypos="113"/>
        </arrow>
        <arrow id="r89" to="r65" navcoords="" colorstyle="color=-12566464 " from="r84" ylabel="-1" fromPortNo="0" ref="r90" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r91" xpos="512" ypos="145"/>
          <coord id="r92" xpos="328" ypos="162"/>
          <coord id="r93" xpos="228" ypos="305"/>
        </arrow>
        <arrow id="r94" to="r65" navcoords="" colorstyle="color=-12566464 " from="r95" ylabel="-1" fromPortNo="0" ref="r96" toPortNo="0" style="curve" xlabel="-1">
          <coord id="r97" xpos="251" ypos="463"/>
          <coord id="r98" xpos="220" ypos="408"/>
          <coord id="r99" xpos="213" ypos="360"/>
        </arrow>
        <box id="r84" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r100" fontstyle="color=-16777216 " height="55" style="color=-96412 ">
          <coord id="r101" xpos="512" ypos="113"/>
        </box>
        <box id="r78" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r9" fontstyle="color=-16777216 " height="55" style="color=-3475580 ">
          <coord id="r102" xpos="151" ypos="88"/>
        </box>
        <box id="r72" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r103" fontstyle="color=-16777216 " height="55" style="color=-96412 ">
          <coord id="r104" xpos="529" ypos="286"/>
        </box>
        <box id="r65" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r105" fontstyle="color=-16777216 " height="55" style="color=-3475580 ">
          <coord id="r106" xpos="154" ypos="305"/>
        </box>
        <box id="r66" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r107" fontstyle="color=-16777216 " height="55" style="color=-5263381 ">
          <coord id="r108" xpos="431" ypos="442"/>
        </box>
        <box id="r95" navcoords="" icon="" width="110" ghost="false" angle="0.0" ref="r109" fontstyle="color=-16777216 " height="55" style="color=-986951 ">
          <coord id="r110" xpos="212" ypos="463"/>
        </box>
      </diagram>
      <exchange id="r111"/>
      <model id="r63" startTime="0.0" timeUnit="nounit" stepSize="0.1" name="Mathematical pendulum" endTime="10.0" externalId="" createdByUser="true">
        <factor id="r100" useInteger="false" paloId="" useDependencies="false" type="level" externalId="" unit="rad" formulaType="manual" paloAggregate="false" formulaText="" description="Auslenkung des Pendels aus der Ruhelage (unterster Punkt des Pendelkreises)." name="Auslenkung" initialValue="0.0" plainDescription="Auslenkung des Pendels aus der Ruhelage (unterster Punkt des Pendelkreises)." startDelayLoop="false" paloType="">
          <simseries id="r19" interpolator="linear"/>
          <xyseries id="r33" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="linear" yunit="" name="Auslenkung" xcoords="">0.0,0.0,1.0,1.0</xyseries>
          <xyseries id="r35" olapElementTime="0" xunit="" olapTimeMap="true" type="expected" interpolator="linear" yunit="" name="Auslenkung (Vergleichswerte 1)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
          <xyseries id="r37" olapElementTime="0" xunit="" olapTimeMap="true" type="desired" interpolator="linear" yunit="" name="Auslenkung (Vergleichswerte 2)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
        </factor>
        <factor id="r9" useInteger="false" paloId="" useDependencies="false" type="rate" externalId="" unit="rad/s" formulaType="manual" paloAggregate="false" formulaText="cos([Impuls])" description="Zeitliche Änderung der Auslenkung des Pendels (eine Art Winkelgeschwindigkeit) als rate." name="Änderung d. Auslenkung" initialValue="NaN" plainDescription="Zeitliche Änderung der Auslenkung des Pendels (eine Art Winkelgeschwindigkeit) als rate." startDelayLoop="false" paloType="">
          <simseries id="r29" interpolator="linear"/>
          <xyseries id="r39" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="linear" yunit="" name="Änderung d. Auslenkung" xcoords="">0.0,0.0,1.06E-4,0.00114,0.00297,0.00381,0.00584,0.00434,0.0231,0.00914,0.0345,0.0131,0.0833,0.026,0.0948,0.0268,0.112,0.0273,0.135,0.0276,0.164,0.0278,0.253,0.0259,0.284,0.0243,0.301,0.0227,0.316,0.0212,0.32,0.0193,0.33,0.0159,0.336,0.0123,0.339,0.00843,0.356,0.00523,0.373,0.00327,0.384,0.00185,0.413,6.05E-4,0.465,4.27E-4,0.534,0.00238,0.631,0.01,0.66,0.0141,0.68,0.0177,0.683,0.0204,0.689,0.0228,0.706,0.025,0.723,0.0266,0.76,0.0276,0.823,0.0278,0.869,0.0276,0.901,0.0269,0.929,0.0253,0.955,0.0232,0.967,0.0189,0.975,0.0154,0.99,0.0125,0.998,0.00986,1.0,0.00754,1.03,0.0047,1.06,0.00166,1.09,0.00182,1.12,0.00182</xyseries>
          <xyseries id="r41" olapElementTime="0" xunit="" olapTimeMap="true" type="expected" interpolator="linear" yunit="" name="Änderung d. Auslenkung (Vergleichswerte 1)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
          <xyseries id="r43" olapElementTime="0" xunit="" olapTimeMap="true" type="desired" interpolator="linear" yunit="" name="Änderung d. Auslenkung (Vergleichswerte 2)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
          <xyseries id="r45" olapElementTime="0" xunit="" olapTimeMap="true" type="dependent" interpolator="linear" yunit="" name="Änderung d. Auslenkung" xcoords="">0.0,0.0,100.0,0.0</xyseries>
        </factor>
        <factor id="r103" useInteger="false" paloId="" useDependencies="false" type="level" externalId="" unit="m" formulaType="manual" paloAggregate="false" formulaText="" description="Zeitliche Änderung der Auslenkung des Pendels (eine Art Winkelgeschwindigkeit) als level." name="Impuls" initialValue="50.0" plainDescription="Zeitliche Änderung der Auslenkung des Pendels (eine Art Winkelgeschwindigkeit) als level." startDelayLoop="false" paloType="">
          <simseries id="r21" interpolator="linear"/>
          <xyseries id="r23" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="linear" yunit="" name="Impuls" xcoords="">0.0,0.0,1.0,1.0</xyseries>
          <xyseries id="r47" olapElementTime="0" xunit="" olapTimeMap="true" type="expected" interpolator="linear" yunit="" name="Impuls (Vergleichswerte 1)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
          <xyseries id="r49" olapElementTime="0" xunit="" olapTimeMap="true" type="desired" interpolator="linear" yunit="" name="Impuls (Vergleichswerte 2)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
        </factor>
        <factor id="r105" useInteger="false" paloId="" useDependencies="false" type="rate" externalId="" unit="m/s²" formulaType="manual" paloAggregate="false" formulaText="sin([Auslenkung])*[Erdbeschleunigung]*[Sinus Approx]" description="Winkelbeschleunigung des Pendels: Eine Funktion der Erdbeschleunigung, der Auslenkung des Pendels und der Hilfsgröße &quot;Sinus Approx&quot;." name="Erdanziehung" initialValue="NaN" plainDescription="Winkelbeschleunigung des Pendels: Eine Funktion der Erdbeschleunigung, der Auslenkung des Pendels und der Hilfsgröße &quot;Sinus Approx&quot;." startDelayLoop="false" paloType="">
          <simseries id="r27" interpolator="linear"/>
          <xyseries id="r51" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="linear" yunit="" name="Erdanziehung" xcoords="">0.0,0.0,0.00567,0.0367,0.0168,0.14,0.0307,0.255,0.053,0.37,0.0558,0.375,0.0864,0.496,0.111,0.57,0.142,0.657,0.167,0.702,0.192,0.725,0.231,0.737,0.259,0.708,0.29,0.645,0.312,0.576,0.329,0.53,0.343,0.49,0.357,0.415,0.37,0.329,0.39,0.22,0.407,0.117,0.429,0.054,0.448,0.0138,0.49,0.0023,0.543,0.054,0.596,0.163,0.627,0.249,0.66,0.37,0.691,0.484,0.719,0.582,0.746,0.639,0.75,0.645,0.788,0.708,0.819,0.754,0.849,0.766,0.886,0.766,0.916,0.771,0.92,0.76,0.939,0.72,0.958,0.645,0.961,0.639,0.986,0.53,1.01,0.438,1.05,0.236</xyseries>
          <xyseries id="r53" olapElementTime="0" xunit="" olapTimeMap="true" type="dependent" interpolator="linear" yunit="" name="Erdanziehung" xcoords="">0.0,0.0,100.0,0.0</xyseries>
          <xyseries id="r55" olapElementTime="0" xunit="" olapTimeMap="true" type="expected" interpolator="linear" yunit="" name="Erdanziehung (Vergleichswerte 1)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
          <xyseries id="r57" olapElementTime="0" xunit="" olapTimeMap="true" type="desired" interpolator="linear" yunit="" name="Erdanziehung (Vergleichswerte 2)" xcoords="">0.0,0.0,1.0,0.0</xyseries>
        </factor>
        <factor id="r107" useInteger="false" paloId="" useDependencies="false" type="auxiliary" externalId="" unit="m/s²" formulaType="manual" paloAggregate="false" formulaText="9.81" description="(Als konstante 9,81 m/s**2 angenommene) Schwerebeschleunigung." name="Erdbeschleunigung" initialValue="NaN" plainDescription="(Als konstante 9,81 m/s**2 angenommene) Schwerebeschleunigung." startDelayLoop="false" paloType="">
          <simseries id="r25" interpolator="linear"/>
          <xyseries id="r59" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="constant" yunit="" name="Erdbeschleunigung" xcoords="">0.0,9.81,1.0,9.81,2.0,9.81,3.0,9.81,140.0,9.81</xyseries>
        </factor>
        <factor id="r109" useInteger="false" paloId="" useDependencies="false" type="auxiliary" externalId="" unit="1/rad" formulaType="manual" paloAggregate="false" formulaText="1.0" description="Hilfsgröße, um der multiplikativen Formel bei &quot;Erdanziehung&quot; Genüge zu leisten.&#10;Daher hat diese Größe den zeitlich konstanten numerischen Wert 1.0/rad. Sie soll&#10;verdeutlichen, daß beim vereinfachten mathematischen Pendel die Approximation sin (phi) = phi&#10;(für kleine Winkel) benutzt wird." name="Sinus Approx" initialValue="NaN" plainDescription="Hilfsgröße, um der multiplikativen Formel bei &quot;Erdanziehung&quot; Genüge zu leisten. Daher hat diese Größe den zeitlich konstanten numerischen Wert 1.0/rad. Sie soll verdeutlichen, daß beim vereinfachten mathematischen Pendel die Approximation sin (phi) = phi (für kleine Winkel) benutzt wird." startDelayLoop="false" paloType="">
          <simseries id="r31" interpolator="linear"/>
          <xyseries id="r61" olapElementTime="0" xunit="" olapTimeMap="true" type="input" interpolator="constant" yunit="" name="Sinus Approx" xcoords="">0.0,1.0,100.0,1.0</xyseries>
        </factor>
        <interaction id="r67" to="r105" staticImpact="100.0" label="100" from="r107" type="information" userLabel="false" description="" polarity="1" name="Erdbeschleunigung --&gt; Erdanziehung" plainDescription="" delay="0.0" delaytype="shortterm"/>
        <interaction id="r73" to="r103" staticImpact="100.0" label="-100" from="r105" type="flow" userLabel="false" description="" polarity="-1" name="Erdanziehung --&gt; Impuls" plainDescription="" delay="0.0" delaytype="shortterm"/>
        <interaction id="r79" to="r9" staticImpact="100.0" label="100" from="r103" type="information" userLabel="false" description="" polarity="1" name="Impuls --&gt; Änderung d. Auslenkung" plainDescription="" delay="0.0" delaytype="shortterm"/>
        <interaction id="r85" to="r100" staticImpact="100.0" label="100" from="r9" type="flow" userLabel="false" description="" polarity="1" name="Änderung d. Auslenkung --&gt; Auslenkung" plainDescription="" delay="0.0" delaytype="shortterm"/>
        <interaction id="r90" to="r105" staticImpact="100.0" label="100" from="r100" type="information" userLabel="false" description="" polarity="1" name="Auslenkung --&gt; Erdanziehung" plainDescription="" delay="0.0" delaytype="shortterm"/>
        <interaction id="r96" to="r105" staticImpact="100.0" label="100" from="r109" type="information" userLabel="false" description="" polarity="1" name="Sinus Approx --&gt; Erdanziehung" plainDescription="" delay="0.0" delaytype="shortterm"/>
      </model>
      <simcockpit id="r17" name="Simulationsergebnisse">
        <chart id="r112" rendererType="lineRenderer" zoomY1="0.0" numberformat="0" timeStamp="" zoomY0="0.0" bins="0" type="crossImpactChartType" height="280" style="color=-2830136 " description="" name="Mathematical pendulum" ypos="20" zoomX1="0.0" zoomX0="0.0" freezed="false" useTimeline="false" width="300" allSelectedRange="false" ref="r113" fontstyle="color=-16777216 " xpos="649" domainAxisLabel="Zeit">
          <curvegroup id="r114" refs="r18 r20"/>
        </chart>
        <chart id="r115" rendererType="lineRenderer" zoomY1="0.0" numberformat="0" timeStamp="" zoomY0="0.0" bins="0" type="ordinaryChartType" height="280" style="color=-2830136 " description="" name="Mathematical pendulum" ypos="19" zoomX1="0.0" zoomX0="0.0" freezed="false" useTimeline="false" width="300" allSelectedRange="false" ref="r113" fontstyle="color=-16777216 " xpos="335" domainAxisLabel="Zeit">
          <curvegroup id="r116" refs="r18"/>
        </chart>
        <chart id="r117" rendererType="lineRenderer" zoomY1="0.0" numberformat="0" timeStamp="" zoomY0="0.0" bins="0" type="ordinaryChartType" height="280" style="color=-2830136 " description="" name="Mathematical pendulum" ypos="17" zoomX1="0.0" zoomX0="0.0" freezed="false" useTimeline="false" width="300" allSelectedRange="false" ref="r113" fontstyle="color=-16777216 " xpos="13" domainAxisLabel="Zeit">
          <curvegroup id="r118" refs="r20"/>
        </chart>
      </simcockpit>
      <simulation id="r113" useBeginning="true" monteCarloAmount="1" endTime="10.0" startTime="0.0" ref="r63" stepSize="0.1" timeUnit="nounit" method="Runge_Kutta_2" dominantPathAnalysis="false"/>
    </scenario>
  </scenarios>
  <sign id="r119" verify="U5F/BW5erxtMQ9OxGabdiNmplcN4V909zDYe/B4nE0+UvP5MAsC4UPWOKimGUgD1gsI1NpmrQXKjgMrEmJXhF6o1vK8q612JOp0mgnlUfce9IPhmu4UnybZVTGOyZghFHGnotpxhWKeM1eC0bu5XTTxr4a622as6WhIMTtNbHMpXLC818h3Y5/6oNG1q40kJX0mL1finLJb+xelPUt38vR6Yq3Wli1bwo5R8660kO9JyLNnzBvpMlZkM1/6ViOIO7IQDosBe8vT2S3HxUhC9hlOpg7vP4+/QLnI6+rnshWOUuGAGm+ydiiM5LccVHZZqjnGNhqAzw7U0W+rAuxzf8kdYWnrv1Tgs3x5JBBlqOvIZ0MXoxDFdkvKQEwEjgyPnYqczK5Uqxl1Y4KPaWHhE/Er3bUl01rJkAeoL/sZNZJ2XaIRygZZ1OIrCP4dmxSlGsbGvItpM4Ot4D+dZtQOj0b9/0rvBcjcS9KFUnOtaL75THmmgcBVyqQ=="/>
</project>
