Applets:Periodendauer periodischer Signale: Difference between revisions

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{{LntExplicitLoadMathjax}}
<p>
{{BlaueBox|TEXT=
<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>
<html>
<html>
<head>
<head>
    <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://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
   <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
    <style>
  <style>
        .button {
  .button1{
            background-color: black;
    background-color: black;
            border: none;
    border: none;
            color: white;
    color: white;
            font-family: arial;
    font-family: arial;
            padding: 8px 20px;
    padding: 8px 20px;
            text-align: center;
    text-align: center;
            text-decoration: none;
    text-decoration: none;
            display: inline-block;
    display: inline-block;
            font-size: 16px;
    font-size: 16px;
            border-radius: 15px;
    border-radius: 15px;
        }
    position:relative;
        .button:active {
    top: 100px;
            background-color: #939393;
    left: 600px;
        }
  }
 
  .button1:active {
    background-color: #939393;}
 


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






<body>
<form id="myForm">
<form id="jxgForm">
 
    <!-- Resetbutton, Checkbox, Regler und Plots -->
<!-- Resetbutton, Checkbox und Formel -->
    <p>
<button class="button1" style="font-size:0.750em" onclick="zurueck()">Reset</button>
        <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien zeigen</label>
<p><span class="separate" style="position:absolute; top:320px; left:725px; font-family:arial; font-size:0.750em;">mit Gitter<input name="gridbox" id="gridbox" type="checkbox" onclick="showgrid();" checked="checked"></span></p>
        <button class="button" onclick="rst()">Reset</button>
    </p>
    <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:100px; float:top; margin:-10px 20px 100px 0px;"></div>
    <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-10px 20px 100px 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>


<div id="box1" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:100px 20px 0px 0px;"></div>
<div id="box2" class="jxgbox" style="width:600px; height:150px; border:1px solid white; margin:-760px 20px 0px 0px;"></div>
<div id="box3" class="jxgbox" style="width:600px; height:100px; border:1px solid white; margin:625px 20px 0px 0px;"></div>


<script type="text/javascript">
<script type="text/javascript">
    // Grundeinstellungen der beiden Applets
    JXG.Options.text.useMathJax = true;
    var 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]
    });
    var pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
        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
//Grundeinstellungen der beiden Applets
    xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
JXG.Options.text.useMathJax = true;
        name: '$\\dfrac{t}{T}$',
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]});
        withLabel: true, label: { position: 'rt', offset: [-25, -10] }
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]});
    });
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]});
    yaxis = pltBox.create('axis', [[0, 0], [0, 1]], {
brd2.addChild(brd1);
        name: '$x(t)$',
brd2.addChild(brd3);
        withLabel: true, label: { position: 'rt', offset: [10, -5] }
    });


    // Erstellen der Schieberegler
//Einstellungen der Achsen
    a = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
xaxis = brd1.create('axis', [[0, 0], [1,0]], {name:'\\[t/T\\]', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
        suffixlabel: '$A_1=$',
yaxis = brd1.create('axis', [[0, 0], [0, 1]], {name:'\\[x(t)\\]', withLabel:true, label:{position:'rt', offset:[10, -5]}});
        unitLabel: 'V', snapWidth: 0.01
        }),
    b = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
        suffixlabel: '$f_1=$',
        unitLabel: 'kHz', snapWidth: 0.1
    }),
    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
//Festlegen der Schieberegler
    signaldarstellung = pltBox.create('functiongraph', [function(x) {
a = brd2.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
        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))
b = brd2.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
    }], {
c = brd2.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {withLabel:false, withTicks:false, snapWidth:5}),
        strokeColor: "red"
d = brd2.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {withLabel:false, withTicks:false, snapWidth:0.01}),
    });
e = brd2.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {withLabel:false, withTicks:false, snapWidth:0.1}),
g = brd2.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {withLabel:false, withTicks:false, snapWidth:5}),
t = brd2.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {withLabel:false, withTicks:false, snapWidth:0.2}),


    // Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
    p_T0 = pltBox.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 = pltBox.create('point',
        [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 Ausgabefelder
    setInterval(function() {
texta=brd2.create('text',[2.8,1.87, function()
        document.getElementById("T_0").innerHTML = Math.round(getT0() * 100) / 100;
  { return '\\[A_1= '+ Math.round(a.Value()*100)/100 +' \\text{ V}\\]';}], {fixed:true, visible:true, fontSize:14});
    }, 50);
textb=brd2.create('text',[2.8,0.87, function()
  { return '\\[f_1= '+ Math.round(b.Value()*100)/100 +' \\text{ kHz}\\]';}], {fixed:true, visible:true, fontSize:14});
textc=brd2.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=brd2.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=brd2.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=brd2.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=brd2.create('text',[2.8,-1.2, function()
  { return '\\[t= '+ Math.round(t.Value()*100)/100 +' \\]';}], {fixed:true, visible:true, fontSize:14});


textergebnis1=brd3.create('text',[-1,1.5, 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, fontSize:14});
textergebnis2=brd3.create('text',[1.5,1.5, function()
  { 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=brd3.create('text',[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, fontSize:14});
textergebnis4=brd3.create('text',[8.5,1.5, 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;};
return '\\[x_{max}= '+ Math.max.apply(Math,x)+' \\]';}], {fixed:true, visible:true, fontSize:14});
textergebnis5=brd3.create('text',[10.8,1.5, function()
  { return '\\[T_0= '+ Math.round(getT0() *100)/100 +' \\]';}], {fixed:true, visible:true, strokeColor:'blue', fontSize:14});


//Definition der Funktion
signaldarstellung = brd1.create('functiongraph',[function(x){
        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))
    }], {strokeColor: "red"});


    function isInt(n) {
//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_0
         return n % 1 === 0;
p_T0=brd1.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 = brd1.create('point', [function(){ return Math.round(getT0() *100)/100;}, 2], {visible: false, color:"blue", fixed:true, label:false, size:1, name:''})
l_T0 = brd1.create('line', [p_T0, p_T0h])


//Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
     function getT0() {
     function getT0() {
         var A, B, C, Q;
         var A, B, C, Q;
         if (b.Value() < e.Value()) {
         if (b.Value() < e.Value()) {
Line 154: Line 127:
             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;
             }
             }
Line 166: Line 141:
                 return 10;
                 return 10;
             }
             }
             if ((1 / C) > 10)
             if ((1/C) > 10)
                 return 10
                 return 10
         }
         }
     }
     }


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




    // Ausgabe des Wertes x(t)
    setInterval(function() {
        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() /
            360)) * 1000) / 1000;
    }, 50);


    // Ausgabe des Wertes x(t+T_0)
//Definition der Funktion zum An- und Ausschalten des Koordinatengitters
    setInterval(function() {
function showgrid() {
        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() +
    if (gridbox.checked) {
            Math.round(getT0() * 1000) / 1000) - g.Value())) * 1000) / 1000;
      xaxis = brd1.create('axis', [[0, 0], [1,0]], {});
    }, 50);
      yaxis = brd1.create('axis', [[0, 0], [0, 1]], {});
    } else {
    xaxis.removeTicks(xaxis.defaultTicks);
    yaxis.removeTicks(yaxis.defaultTicks);
    }
    brd1.fullUpdate();
};
</script>
</form>


    // Ausgabe des Wertes x(t+2T_0)
<script>
    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 des Reset-Buttons
function zurueck() {
    document.getElementById("myForm").reset();
};
</script>


</body>
</html>


    // 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
{{Display}}
    function rst() {
        document.getElementById("jxgForm").reset();
    };
</script>
</body>
</html>

Revision as of 18:15, 13 September 2017

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


mit Gitter



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