Applets:Periodendauer periodischer Signale: Unterschied zwischen den Versionen

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<p>
 
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{{BlaueBox|TEXT=
 
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<B style="font-size:18px">Funktion:</B>
 
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$$x(t) = A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)$$
 
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</p>
 
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<html>
 
<html>
 
<head>
 
<head>
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    <meta charset="utf-8" />
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  <script type="text/javascript" src="http://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script>
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    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script>
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  <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
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    <!-- <script type="text/javascript" src="https://www.lntwww.de/MathJax/unpacked/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full,local/mwMathJaxConfig"></script> -->
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  <style>
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    <!-- <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script> -->
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  .button1{
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<style>
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    background-color: black;
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        .button {
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    border: none;
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            background-color: black;
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    color: white;
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            border: none;
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    font-family: arial;
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            color: white;
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    padding: 8px 20px;
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            font-family: arial;
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    text-align: center;
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            padding: 8px 20px;
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    text-decoration: none;
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            text-align: center;
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    display: inline-block;
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            text-decoration: none;
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    font-size: 16px;
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            display: inline-block;
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    border-radius: 15px;
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            font-size: 16px;
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    position:relative;
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            border-radius: 15px;
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    top: 205px;
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        }
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    left: 530px;
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        .button:active {
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  }
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            background-color: #939393;
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         }
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  .button1:active {
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    background-color: #939393;}
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    .formel {
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        background-color: #f5f5f5;
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         border-radius: 4px ;
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        padding: 20px 30px;
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        font-family: arial;
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        position:absolute;
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        top: 250px;
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        left: 10px;
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    }
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   </style>
 
   </style>
 
</head>
 
</head>
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<body>
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<form id="myForm">
  
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<body>
 
 
<!-- Resetbutton, Checkbox und Formel -->
 
<!-- Resetbutton, Checkbox und Formel -->
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<button class="button1" style="font-size:0.750em" onclick="zurueck()">Reset</button>
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<p><span class="separate" style="position:absolute; top:180px; left:550px; font-family:arial; font-size:0.750em;">mit Gitter<input name="gridbox" id="gridbox" type="checkbox" onclick="showgrid();" checked="checked"></span></p>
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<box class="formel">\(x(t)=A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)\)</box>
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<div id="box1" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:300px 20px 100px 0px;"></div>
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<div id="box2" class="jxgbox" style="width:500px; height:200px; border:1px solid white; margin:-1000px 20px 100px 0px;"></div>
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<div id="box3" class="jxgbox" style="width:600px; height:100px; border:1px solid white; margin:700px 20px 100px 0px;"></div>
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<script type="text/javascript">
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 +
//Grundeinstellungen der beiden Applets
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JXG.Options.text.useMathJax = true;
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var brd1 = JXG.JSXGraph.initBoard('box1', {showCopyright:false, axis:false, zoom:{factorX:1.1, factorY:1.1, wheel:true, needshift:true, eps: 0.1}, grid:false, boundingbox: [-0.5, 2.2, 12.4, -2.2]});
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var brd2 = JXG.JSXGraph.initBoard('box2', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
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var brd3 = JXG.JSXGraph.initBoard('box3', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
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brd2.addChild(brd1);
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brd2.addChild(brd3);
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 +
//Einstellungen der Achsen
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xaxis = brd1.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
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yaxis = brd1.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}});
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//Festlegen der Schieberegler
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a = brd2.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
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b = brd2.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
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c = brd2.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}),
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d = brd2.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
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e = brd2.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
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g = brd2.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}),
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t = brd2.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}),
  
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<div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px;  float:top; margin:-10px 20px 100px 0px;"></div>
 
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<div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-100px 20px 10px 0px;"></div>
 
  
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//Definition der Ausgabefelder
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texta=brd2.create('text',[3.2,1.7, function()
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  { return '\\[A_1= '+ Math.round(a.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true});
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textb=brd2.create('text',[3.2,0.7, function()
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  { return '\\[f_1= '+ Math.round(b.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true});
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textc=brd2.create('text',[3.2,-0.3, function()
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  { return '\\[\\phi_1= '+ Math.round(c.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true});
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textd=brd2.create('text',[9.9,1.57, function()
 +
  { return '\\[A_2= '+ Math.round(d.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true});
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texte=brd2.create('text',[9.9,0.57, function()
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  { return '\\[f_2= '+ Math.round(e.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true});
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textg=brd2.create('text',[9.9,-0.43, function()
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  { return '\\[\\phi_2= '+ Math.round(g.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true});
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textt=brd2.create('text',[3.2,-1.3, function()
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  { return '\\[t= '+ Math.round(t.Value()*100)/100 +' \\]';}], {fixed:true, visible:true});
  
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textergebnis1=brd3.create('text',[-0.5,1.5, function()
 +
  { return '\\[x(t)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*t.Value()-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*t.Value()-2*Math.PI*g.Value()/360))*1000)/1000 +' \\]';}], {fixed:true, visible:true});
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textergebnis2=brd3.create('text',[1.6,1.5, function()
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  { return '\\[x(t+T_0)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(t.Value()+Math.round(getT0() *1000)/1000)-c.Value())+d.Value()*Math.cos(2*Math.PI*e.Value()*(t.Value()+Math.round(getT0() *1000)/1000)-g.Value()))*1000)/1000 +' \\]';}], {fixed:true, visible:true});
 +
textergebnis3=brd3.create('text',[4.5,1.5, function()
 +
  { return '\\[x(t+2T_0)= '+ Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(t.Value()+2*Math.round(getT0() *1000)/1000)-c.Value())+d.Value()*Math.cos(2*Math.PI*e.Value()*(t.Value()+2*Math.round(getT0() *1000)/1000)-g.Value()))*1000)/1000 +' \\]';}], {fixed:true, visible:true});
 +
textergebnis4=brd3.create('text',[7.75,1.5, function()
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{var x = new Array(50000);
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for (var i = 0; i < 50001; i++) {x[i] = Math.round((a.Value()*Math.cos(2*Math.PI*b.Value()*(i/1000)-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*(i/1000)-2*Math.PI*g.Value()/360)) *1000)/1000;};
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return '\\[x_{max}= '+ Math.max.apply(Math,x)+' \\]';}], {fixed:true, visible:true});
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textergebnis5=brd3.create('text',[10.5,1.5, function()
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  { return '\\[T_0= '+ Math.round(getT0() *100)/100 +' \\]';}], {fixed:true, visible:true, strokeColor:'blue'});
  
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<script type="text/javascript">
 
  
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        // Grundeinstellungen der beiden Applets
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//Definition der Funktion
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         JXG.Options.text.useMathJax = true;
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signaldarstellung = brd1.create('functiongraph',[function(x){
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        cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {
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         return (a.Value()*Math.cos(2*Math.PI*b.Value()*x-2*Math.PI*c.Value()/360)+d.Value()*Math.cos(2*Math.PI*e.Value()*x-2*Math.PI*g.Value()/360))
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            showCopyright: false, showNavigation: false, axis: false,
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    }], {strokeColor: "red"});
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            grid: false, zoom: { enabled: false }, pan: { enabled: false },
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            boundingbox: [-1, 2.2, 12.4, -2.2]
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//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
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         });
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p_T0=brd1.create('point', [function(){ return Math.round(getT0() *100)/100;},
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        pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
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      function(){ return a.Value()*Math.cos(2*Math.PI*b.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*c.Value()/360)
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             showCopyright: false, axis: true,
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        +d.Value()*Math.cos(2*Math.PI*e.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*g.Value()/360);}], {color:"blue", fixed:true, label:false, size:1, name:''})
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             zoom: { factorX: 1.1, factorY: 1.1, wheel: true, needshift: true, eps: 0.1 },
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p_T0h = brd1.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''})
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            grid: true, boundingbox: [-0.5, 2.2, 12.4, -2.2]
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l_T0 = brd1.create('line', [p_T0, p_T0h])
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        });
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        cnfBox.addChild(pltBox);
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//Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
 +
    function getT0() {
 +
 
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        var A, B, C, Q;
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        if (b.Value() < e.Value()) {
 +
            A = b.Value();
 +
            B = e.Value();
 +
         } else {
 +
            B = b.Value();
 +
            A = e.Value();
 +
        }
 +
 
 +
        console.log('Berechne T0 mit A=' + A, 'B=' + B);
 +
 
 +
        for (var x = 1; x <= 100; x++) {
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             C = A / x;
 +
            Q = B / C;
 +
            console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q);
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            if (isInt(Q)) {
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                console.log('Q ist eine Qanzzahl!!! T0 ist damit ', 1 / C);
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                return 1 / C;
 +
             }
 +
            if (x === 10) {
 +
                return 10;
 +
            }
 +
            if ((1/C) > 10)
 +
                return 10
 +
        }
 +
    }
 +
 
 +
    function isInt(n) {
 +
        return n % 1 === 0;
 +
    }
 +
 
 +
 
 +
 
 +
//Definition der Funktion zum An- und Ausschalten des Koordinatengitters
 +
function showgrid() {
 +
    if (gridbox.checked) {
 +
      xaxis = brd1.create('axis', [[0, 0], [1,0]], {});
 +
      yaxis = brd1.create('axis', [[0, 0], [0, 1]], {});
 +
    } else {
 +
    xaxis.removeTicks(xaxis.defaultTicks);
 +
    yaxis.removeTicks(yaxis.defaultTicks);
 +
    }
 +
    brd1.fullUpdate();
 +
};
 +
</script>
 +
</form>
 +
 
 +
<script>
  
 +
//Definition des Reset-Buttons
 +
function zurueck() {
 +
    document.getElementById("myForm").reset();
 +
};
 
</script>
 
</script>
 +
 
</body>
 
</body>
 
</html>
 
</html>
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{{Display}}
 

Version vom 18. September 2017, 23:05 Uhr

mit Gitter

\(x(t)=A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)\)

Abgerufen von „http://www.lntwww.de/index.php?title=Applets:Periodendauer_periodischer_Signale&oldid=15045“
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