Applets:Periodendauer periodischer Signale: Difference between revisions

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<html>
<html>
<head>
<head>
   <script type="text/javascript"
   <script type="text/javascript" src="http://cdnjs.cloudflare.com/ajax/libs/jsxgraph/0.99.6/jsxgraphcore.js"></script>
  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>
   <style>
   <style>
   .button1{
   .button1{
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     top: 105px;
     top: 105px;
     left: 530px;
     left: 530px;
}
  }
 
   .button1:active {
   .button1:active {
     background-color: #939393;}
     background-color: #939393;}


     .hinweis1 {
     .formel {
         background-color: #f5f5f5;
         background-color: #f5f5f5;
         border-radius: 4px ;
         border-radius: 4px ;
         padding: 20px 60px;
         padding: 20px 40px;
        font-family: arial;
        position:absolute;
        top: 150px;
        left: 10px;
    }
    .text5 {
         font-family: arial;
         font-family: arial;
        color:blue;
        font-size:0.75em;
         position:absolute;
         position:absolute;
         top: 159px;
         top: 860px;
        left: 480px;
    }
 
    .text2 {
        font-family: arial;
        font-size:0.75em;
        position:absolute;
        top: 860px;
         left: 100px;
         left: 100px;
    }
    .text3 {
        font-family: arial;
        font-size:0.75em;
        position:absolute;
        top: 860px;
        left: 220px;
    }
    .text4 {
        font-family: arial;
        font-size:0.75em;
        position:absolute;
        top: 860px;
        left: 360px;
    }
    .text1 {
        font-family: arial;
        font-size:0.75em;
        position:absolute;
        top: 860px;
        left: 20px;
     }
     }


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<form id="myForm">
<form id="myForm">


 
<!-- Resetbutton, Checkbox und Formel -->
<h2 class="text" style="color:#939393; font-weight:bold; top:-10px; left:90px; font-family:arial; font-size:1.5em;position:absolute;">Periodendauer <I>T</I><sub>0</sub> periodischer Signale</h2>
 
<button class="button1" style="font-size:0.750em" onclick="zurueck()">Reset</button>
<button class="button1" style="font-size:0.750em" onclick="zurueck()">Reset</button>
<p><span class="separate" style="position:absolute; top:123px; left:454px; font-family:arial; font-size:0.750em;">mit Gitter<input name="gridbox" id="gridbox" type="checkbox" onclick="showgrid();" checked="checked"></span></p>
<p><span class="separate" style="position:absolute; top:123px; left:454px; font-family:arial; font-size:0.750em;">mit Gitter<input name="gridbox" id="gridbox" type="checkbox" onclick="showgrid();" checked="checked"></span></p>
<box class="hinweis1"> </box>
<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>
<!-- Festlegen der Ausgabefelder -->
<div class="text1">
    <span><I>x(t)</I>=<span id="x(t)"></span></span>
</div>
<div class="text2">
    <span><I>x(t+T</I><sub>0</sub><I>)</I>=<span id="x(t+T_0)"></span></span>
</div>
<div class="text3">
    <span><I>x(t+2T</I><sub>0</sub><I>)</I>=<span id="x(t+2T_0)"> </span></span>
</div>
<div class="text4">
    <span><I>x</I><sub>max</sub>=<span id="x_max"></span></span>
</div>
<div class="text5">
    <span><I>T</I><sub>0</sub>=<span id="T_0"></span></span>
</div>
<div id="box2" class="jxgbox" style="width:500px; height:100px; float:top; margin:-10px 20px 100px 0px;"></div>
<div id="box2" class="jxgbox" style="width:500px; height:100px; float:top; margin:-10px 20px 100px 0px;"></div>
<div id="box1" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-10px 20px 100px 0px;"></div>
<div id="box1" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-10px 20px 100px 0px;"></div>
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<script type="text/javascript">
<script type="text/javascript">


//Grundeinstellungen der beiden Applets
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 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 brd1 = JXG.JSXGraph.initBoard('box1', {showCopyright:false, axis:false, grid:false, boundingbox: [-0.9, 2.2, 12.4, -2.2]});
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]});
brd2.addChild(brd1);
brd2.addChild(brd1);


xaxis = brd1.create('axis', [[0, 0], [1,0]], {name:'<I>t</I>/ms', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
//Einstellungen der Achsen
yaxis = brd1.create('axis', [[0, 0], [0, 1]], {name:'<I>x(t)</I>/V', withLabel:true, label:{position:'rt', offset:[10, -5]}});
xaxis = brd1.create('axis', [[0, 0], [1,0]], {name:'<I>t</I>/<I>T</I>', withLabel:true, label:{position:'rt', offset:[-25, 15]}});
yaxis = brd1.create('axis', [[0, 0], [0, 1]], {name:'<I>x(t)</I>', withLabel:true, label:{position:'rt', offset:[10, -5]}});


//Festlegen der Schieberegler
a = brd2.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {suffixlabel:' <I>A</I>_1=', unitLabel: 'V', snapWidth:0.01}),
a = brd2.create('slider',[[-0.7,1.5],[3,1.5],[0,0.5,1]], {suffixlabel:' <I>A</I>_1=', unitLabel: 'V', snapWidth:0.01}),
b = brd2.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {suffixlabel:'<I>f</I>_1=', unitLabel: 'kHz', snapWidth:0.1}),
b = brd2.create('slider',[[-0.7,0.5],[3,0.5],[0,1,10]], {suffixlabel:'<I>f</I>_1=', unitLabel: 'kHz', snapWidth:0.1}),
c = brd2.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {suffixlabel:'<I>&phi;</I>_1=', unitLabel: 'Grad', snapWidth:1}),
c = brd2.create('slider',[[-0.7,-0.5],[3,-0.5],[-180,0,180]], {suffixlabel:'<I>&straightphi;</I>_1=', unitLabel: 'Grad', snapWidth:5}),
d = brd2.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {suffixlabel:'<I>A</I>_2=', unitLabel: 'V', snapWidth:0.01}),
d = brd2.create('slider',[[6,1.5],[9.7,1.5],[0,0.5,1]], {suffixlabel:'<I>A</I>_2=', unitLabel: 'V', snapWidth:0.01}),
e = brd2.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {suffixlabel:'<I>f</I>_2=', unitLabel: 'kHz', snapWidth:0.1}),
e = brd2.create('slider',[[6,0.5],[9.7,0.5],[0,2,10]], {suffixlabel:'<I>f</I>_2=', unitLabel: 'kHz', snapWidth:0.1}),
g = brd2.create('slider',[[6,-0.5],[9.7,-0.5],[-179,90,180]], {suffixlabel:'<I>&phi;</I>_2=',unitLabel: 'Grad', snapWidth:5}),
g = brd2.create('slider',[[6,-0.5],[9.7,-0.5],[-180,90,180]], {suffixlabel:'<I>&straightphi;</I>_2=',unitLabel: 'Grad', snapWidth:5}),
t = brd2.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {suffixlabel:'<I>t</I>=', unitLabel: 'ms',snapWidth:0.01}),
t = brd2.create('slider',[[-0.7,-1.5],[3,-1.5],[0,0,10]], {suffixlabel:'<I>t</I>=', snapWidth:0.2}),
 
//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"});
 
//Definition des Punktes p_T0, des Hilfspunktes p_T0h und der Geraden l_T0 für Periodendauer T_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
setInterval(function() {
var y=Math.round(getT0() *100)/100
document.getElementById("T_0").innerHTML = y;
}, 0.1);
 
    function getT0() {
 
        var A, B, C, Q;
        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++) {
            C = A / x;
            Q = B / C;
            console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q);
            if (isInt(Q)) {
                console.log('Q ist eine Qanzzahl!!! T0 ist damit ', 1 / C);
                return 1 / C;
            }
            if (x === 10) {
                return 10;
            }
            if ((1/C) > 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;
}, 0.1);


//Ausgabe des Wertes x(t+T_0)
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()+Math.round(getT0() *1000)/1000)-g.Value()))*1000)/1000;
}, 0.1);


brd2.createElement('text', [6.95,-1.48, "V"], {fixed:true});
//Ausgabe des Wertes x(t+2T_0)
brd2.createElement('text', [7.8,-1.6, "<I>T</I>_0="], {fixed:true});
setInterval(function() {
brd2.create('text',[5.4,-1.48, 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;
  { return '<I>x(t)</I>='+(a.Value()*Math.cos(2*Math.PI*b.Value()*t.Value()-c.Value())+d.Value()*Math.cos(2*Math.PI*e.Value()*t.Value()-g.Value())).toFixed(3) ;}], {fixed:true});
}, 0.1);


signaldarstellung = brd1.create('functiongraph',[function(x){
//Ausgabe des Wertes x_max
         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))
setInterval(function() {
    },0], {strokeColor: "red"});
  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);
}, 0.1);


//Definition der Funktion zum An- und Ausschalten des Koordinatengitters
function showgrid() {
function showgrid() {
     if (gridbox.checked) {
     if (gridbox.checked) {
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     brd1.fullUpdate();
     brd1.fullUpdate();
};
};
</script>
</script>
</form>
</form>


<script>


<script>
//Definition des Reset-Buttons
function zurueck() {
function zurueck() {
     document.getElementById("myForm").reset();
     document.getElementById("myForm").reset();
}
};
</script>
</script>


Revision as of 21:26, 9 September 2017

Erklärung.

<applet>


mit Gitter

\(x(t)=A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)\)
x(t)=
x(t+T0)=
x(t+2T0)=
xmax=
T0=



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