Applets:Periodendauer periodischer Signale: Difference between revisions

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{{LntExplicitLoadMathjax}}
<p>
<p>
{{BlaueBox|TEXT=
{{BlaueBox|TEXT=
$x(t) = A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)$
<B style="font-size:18px">Funktion:</B>
$$x(t) = A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)$$
}}
}}
</p>
</p>
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<html>
<html>
<head>
<head>
    <meta charset="utf-8" />
  <meta charset="utf-8" />
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script>
  <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script>
    <!-- <script type="text/javascript" src="https://en.lntwww.de/MathJax/unpacked/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full,local/mwMathJaxConfig"></script> -->
  <!-- <script type="text/javascript" src="https://en.lntwww.de/MathJax/unpacked/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full,local/mwMathJaxConfig"></script> -->
    <style>
  <!-- <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script> -->
 
<style>
         .button {
         .button {
             background-color: black;
             background-color: black;
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         }
         }


        table {
  </style>
            border-collapse: separate;
            border-spacing: 20px 0;
        }
    </style>
</head>
</head>






<body>
<body onload="drawNow()">
<form id="jxgForm">
<!-- Resetbutton, Checkbox und Formel -->
    <!-- Resetbutton, Checkbox, Regler und Plots -->
<p>
    <p>
    <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien zeigen</label>
        <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien Zeigen</label>
    <button class="button" onclick="drawNow();">Reset</button>
        <button class="button" onclick="rst()">Reset</button>
</p>
    </p>
<div id="plotBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:170px 20px 0px 0px;"></div>
    <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:100px; float:top; margin:-10px 20px 100px 0px;"></div>
<div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px; margin:-760px 20px 0px 0px;"></div>
    <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-10px 20px 100px 0px;"></div>
<div id="outBoxHtml" class="jxgbox" style="width:600px; height:100px; margin:625px 20px 0px 0px;"></div>
</form>
 
<!-- Ausgabefelder -->
<table>
    <tr>
        <td>$x(t)$=    <span id="x(t)"></span>    </td>
        <td>$x(t+ T_0)$=<span id="x(t+T_0)"></span> </td>
        <td>$x(t+2T_0)$=<span id="x(t+2T_0)"></span></td>
    </tr>
    <tr>
        <td>$x_{\text{max}}$=<span id="x_max"></span></td>
        <td>$T_0$=          <span id="T_0"></span>  </td>
    </tr>
</table>
 


<script type="text/javascript">
<script type="text/javascript">
    // Grundeinstellungen der beiden Applets
function drawNow() {
    JXG.Options.text.useMathJax = true;
//Grundeinstellungen der beiden Applets
cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {
JXG.Options.text.useMathJax = true;
        showCopyright: false, showNavigation: false, axis: false,
plotBox = JXG.JSXGraph.initBoard('plotBoxHtml', {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]});
        grid: false, zoom: { enabled: false }, pan: { enabled: false },
cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
        boundingbox: [-1, 2.2, 12.4, -2.2]
var outBox = JXG.JSXGraph.initBoard('outBoxHtml', {showCopyright:false, showNavigation:false, axis:false, grid:false, zoom:{enabled:false}, pan:{enabled:false}, boundingbox: [-1, 2.2, 12.4, -2.2]});
    });
cnfBox.addChild(plotBox);
pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
cnfBox.addChild(outBox);
        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]
    });
    cnfBox.addChild(pltBox);


    // Einstellungen der Achsen
//Einstellungen der Achsen
    xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
xaxis = plotBox.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
        name: '$\\dfrac{t}{T}$',
yaxis = plotBox.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}});
        withLabel: true, label: { position: 'rt', offset: [-25, -10] }
    });
    yaxis = pltBox.create('axis', [[0, 0], [0, 1]], {
        name: '$x(t)$',
        withLabel: true, label: { position: 'rt', offset: [10, -5] }
    });


    // Erstellen der Schieberegler
//Festlegen der Schieberegler
    a = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
a = cnfBox.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
        suffixlabel: '$A_1=$',
b = cnfBox.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
        unitLabel: 'V', snapWidth: 0.01
c = cnfBox.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}),
        }),
d = cnfBox.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
    b = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
e = cnfBox.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
        suffixlabel: '$f_1=$',
g = cnfBox.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}),
        unitLabel: 'kHz', snapWidth: 0.1
t = cnfBox.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}),
    }),
    c = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], {
        suffixlabel: '$\\phi_1=$',
        unitLabel: 'Grad', snapWidth: 5
    }),
    d = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], {
        suffixlabel: '$A_2=$',
        unitLabel: 'V', snapWidth: 0.01
    }),
    e = cnfBox.create('slider', [ [6, 0.5], [9.7, 0.5], [0, 2, 10] ], {
        suffixlabel: '$f_2=$',
        unitLabel: 'kHz', snapWidth: 0.1
    }),
    g = cnfBox.create('slider', [ [6, -0.5], [9.7, -0.5], [-180, 90, 180] ], {
        suffixlabel: '$\\phi_2=$',
        unitLabel: 'Grad', snapWidth: 5
    }),
    t = cnfBox.create('slider', [ [-0.7, -1.5], [3, -1.5], [0, 0, 10] ], {
        suffixlabel: '$t=$',
        unitLabel: 's', snapWidth: 0.2
    }),


    // Definition der Funktion
//Definition der Ausgabefelder
    signaldarstellung = pltBox.create('functiongraph', [function(x) {
texta=cnfBox.create('text',[2.8,1.87, function()
        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))
  { return '\\[A_1= '+ Math.round(a.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true, fontSize:14});
    }], {
textb=cnfBox.create('text',[2.8,0.87, function()
        strokeColor: "red"
  { return '\\[f_1= '+ Math.round(b.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true, fontSize:14});
    });
textc=cnfBox.create('text',[2.8,-0.13, function()
  { return '\\[\\phi_1= '+ Math.round(c.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true, fontSize:14});
textd=cnfBox.create('text',[9.5,1.67, function()
  { return '\\[A_2= '+ Math.round(d.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true, fontSize:14});
texte=cnfBox.create('text',[9.5,0.67, function()
  { return '\\[f_2= '+ Math.round(e.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true, fontSize:14});
textg=cnfBox.create('text',[9.5,-0.33, function()
  { return '\\[\\phi_2= '+ Math.round(g.Value()*100)/100 +' \\text{ Grad}\\]';}], {fixed:true, visible:true, fontSize:14});
textt=cnfBox.create('text',[2.8,-1.2, function()
  { return '\\[t= '+ Math.round(t.Value()*100)/100 +' \\]';}], {fixed:true, visible:true, fontSize:14});


    // Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
textergebnis1=outBox.create('text',[-1,1.5, function()
    p_T0 = pltBox.create('point', [
  { 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, fontSize:14});
        function() {
textergebnis2=outBox.create('text',[1.5,1.5, function()
            return (Math.round(getT0() * 100) / 100);
  { 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, fontSize:14});
        },
textergebnis3=outBox.create('text',[5,1.5, function()
        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, fontSize:14});
            return a.Value() * Math.cos(2 * Math.PI * b.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * c.Value() / 360) +
textergebnis4=outBox.create('text',[8.5,1.5, function()
                d.Value() * Math.cos(2 * Math.PI * e.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * g.Value() / 360);
{var x = new Array(50000);
        }],
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;};
        { color: "blue", fixed: true, label: false, size: 1, name: '' }
return '\\[x_{max}= '+ Math.max.apply(Math,x)+' \\]';}], {fixed:true, visible:true, fontSize:14});
    );
textergebnis5=outBox.create('text',[10.8,1.5, function()
    p_T0h = pltBox.create('point',
  { return '\\[T_0= '+ Math.round(getT0() *100)/100 +' \\]';}], {fixed:true, visible:true, strokeColor:'blue', fontSize:14});
        [function() { return (Math.round(getT0() * 100) / 100); }, 2],
        { visible: false, color: "blue", fixed: true, label: false, size: 1, name: '' }
    );
    l_T0 = pltBox.create('line', [p_T0, p_T0h])


    // Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
//Definition der Funktion
    setInterval(function() {
signaldarstellung = plotBox.create('functiongraph',[function(x){
         document.getElementById("T_0").innerHTML = Math.round(getT0() * 100) / 100;
         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))
     }, 50);
     }], {strokeColor: "red"});


//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
p_T0=plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;},
      function(){ return a.Value()*Math.cos(2*Math.PI*b.Value()*(Math.round(getT0() *100)/100)-2*Math.PI*c.Value()/360)
        +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:''})
p_T0h = plotBox.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''})
l_T0 = plotBox.create('line', [p_T0, p_T0h])


};
//Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
    function getT0() {


    function isInt(n) {
        return n % 1 === 0;
    }
    function getT0() {
         var A, B, C, Q;
         var A, B, C, Q;
         if (b.Value() < e.Value()) {
         if (b.Value() < e.Value()) {
Line 162: Line 121:
             A = e.Value();
             A = e.Value();
         }
         }
         // console.log('Berechne T0 mit A=' + A, 'B=' + B);
 
         console.log('Berechne T0 mit A=' + A, 'B=' + B);
 
         for (var x = 1; x <= 100; x++) {
         for (var x = 1; x <= 100; x++) {
             C = A / x;
             C = A / x;
             Q = B / C;
             Q = B / C;
             // console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q);
             console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q);
             if (isInt(Q)) {
             if (isInt(Q)) {
                 // console.log('Q ist eine Ganzzahl!!! T0 ist damit ', 1 / C);
                 console.log('Q ist eine Qanzzahl!!! T0 ist damit ', 1 / C);
                 return 1 / C;
                 return 1 / C;
             }
             }
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                 return 10;
                 return 10;
             }
             }
             if ((1 / C) > 10)
             if ((1/C) > 10)
                 return 10
                 return 10
         }
         }
     }
     }


    function isInt(n) {
        return n % 1 === 0;
    }


 
//Definition der Funktion zum An- und Ausschalten des Koordinatengitters
    // Ausgabe des Wertes x(t)
function showgrid() {
    setInterval(function() {
    if (gridbox.checked) {
        document.getElementById("x(t)").innerHTML = 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() /
      xaxis = plotBox.create('axis', [[0, 0], [1,0]], {});
            360)) * 1000) / 1000;
      yaxis = plotBox.create('axis', [[0, 0], [0, 1]], {});
    }, 50);
    } else {
 
    xaxis.removeTicks(xaxis.defaultTicks);
    // Ausgabe des Wertes x(t+T_0)
    yaxis.removeTicks(yaxis.defaultTicks);
    setInterval(function() {
    }
        document.getElementById("x(t+T_0)").innerHTML = 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() +
    plotBox.fullUpdate();
            Math.round(getT0() * 1000) / 1000) - g.Value())) * 1000) / 1000;
};
    }, 50);
 
    // Ausgabe des Wertes x(t+2T_0)
    setInterval(function() {
        document.getElementById("x(t+2T_0)").innerHTML = 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;
    }, 50);
 
    // Ausgabe des Wertes x_max
    setInterval(function() {
        var x = new Array(50000);
        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;
        }
        document.getElementById("x_max").innerHTML = Math.max.apply(Math, x);
    }, 50);
 
 
 
    // Definition der Funktion zum An- und Ausschalten des Koordinatengitters
    function showgrid() {
        if (gridbox.checked) {
            xaxis = pltBox.create('axis', [ [0, 0], [1, 0] ], {});
            yaxis = pltBox.create('axis', [ [0, 0], [0, 1] ], {});
        } else {
            xaxis.removeTicks(xaxis.defaultTicks);
            yaxis.removeTicks(yaxis.defaultTicks);
        }
        pltBox.fullUpdate();
    };
 
    // Definition des Reset-Buttons
    function rst() {
        document.getElementById("jxgForm").reset();
    };
</script>
</script>
</body>
</body>
</html>
</html>
{{Display}}

Revision as of 09:56, 18 September 2017

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

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