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| | {{LntAppletLink|periode}} |
| | Dieses Applet beschreibt ... |
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| <p> | | <p> |
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| </p> | | </p> |
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| <html>
| | {{LntAppletLink|periode}} |
| <head>
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| <meta charset="utf-8" />
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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://en.lntwww.de/MathJax/unpacked/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full,local/mwMathJaxConfig"></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-full"></script> -->
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| <style>
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| .wrapper1{
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| display:grid;
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| grid-row-gap:1em;
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| justify-items:stretch;
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| align-items:stretch;
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| }
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| .wrapper1 >div{
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| padding:0em;
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| }
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| .wrapper1 >div:nth-child(odd){
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| }
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| .wrapper2{
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| display:grid;
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| grid-row-gap:1em;
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| grid-template-columns:70% 30%;
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| justify-items:stretch;
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| align-items:stretch;
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| }
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| .wrapper2 >div{
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| padding:0em;
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| grid-template-columns:repeat(2);}
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| .box4{
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| grid-column:1/3;
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| grid-row:4/4;
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| border: 1px solid black;
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| }
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| .box5{
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| grid-column:2/3;
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| grid-row:4/4;
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| border: 1px solid black;
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| }
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| .button {
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| background-color: black;
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| border: none;
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| color: white;
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| font-family: arial;
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| padding: 8px 20px;
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| text-align: center;
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| text-decoration: none;
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| display: inline-block;
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| font-size: 16px;
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| border-radius: 15px;
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| }
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| .button:active {
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| background-color: #939393;
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| }
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| </style>
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| </head>
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| <body onload="drawNow()">
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| <!-- Resetbutton, Checkbox und Formel -->
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| <div class="wrapper1">
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| <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px; "></div>
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| <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black;"></div>
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| </div>
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| <!-- Ausgabefelder -->
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| <div class="wrapper2">
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| <div>
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| <table>
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| <tr>
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| <td>$x(t)$= <span id="x(t)"></span> $\quad$ </td>
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| <td>$x(t+ T_0)$= <span id="x(t+T_0)"></span> $\quad$ </td>
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| <td>$x(t+2T_0)$= <span id="x(t+2T_0)"></span> $\quad$ </td>
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| <td>$x_{\text{max}}$= <span id="x_max"></span> $\quad$ </td>
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| <td style="color:blue;">$T_0$= <span id="T_0"></span> $\quad$ </td>
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| </tr>
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| </table>
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| </div>
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| <div>
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| <p>
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| <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien zeigen</label>
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| <button class="button" onclick="drawNow();">Reset</button>
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| </p>
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| </div>
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| </div>
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| <script type="text/javascript">
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| function drawNow() {
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| // Grundeinstellungen der beiden Applets
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| JXG.Options.text.useMathJax = true;
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| cnfBox = JXG.JSXGraph.initBoard('cnfBoxHtml', {
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| showCopyright: false, showNavigation: false, axis: false,
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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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| });
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| pltBox = JXG.JSXGraph.initBoard('pltBoxHtml', {
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| showCopyright: false, axis: false,
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| zoom: { factorX: 1.1, factorY: 1.1, wheel: true, needshift: true, eps: 0.1 },
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| grid: false, boundingbox: [-0.5, 2.2, 12.4, -2.2]
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| });
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| cnfBox.addChild(pltBox);
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| // Einstellungen der Achsen
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| xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
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| name: '$\\dfrac{t}{T}$',
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| withLabel: true, label: { position: 'rt', offset: [-25, -10] }
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| });
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| yaxis = pltBox.create('axis', [[0, 0], [0, 1]], {
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| name: '$x(t)$',
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| withLabel: true, label: { position: 'rt', offset: [10, -5] }
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| });
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| // Erstellen der Schieberegler
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| sldA1 = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
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| suffixlabel: '$A_1=$',
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| unitLabel: 'V', snapWidth: 0.01
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| }),
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| sldF1 = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
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| suffixlabel: '$f_1=$',
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| unitLabel: 'kHz', snapWidth: 0.1
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| }),
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| sldPHI1 = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], {
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| suffixlabel: '$\\phi_1=$',
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| unitLabel: 'Grad', snapWidth: 5
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| }),
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| sldA2 = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], {
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| suffixlabel: '$A_2=$',
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| unitLabel: 'V', snapWidth: 0.01
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| }),
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| sldF2 = cnfBox.create('slider', [ [6, 0.5], [9.7, 0.5], [0, 2, 10] ], {
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| suffixlabel: '$f_2=$',
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| unitLabel: 'kHz', snapWidth: 0.1
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| }),
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| sldPHI2 = cnfBox.create('slider', [ [6, -0.5], [9.7, -0.5], [-180, 90, 180] ], {
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| suffixlabel: '$\\phi_2=$',
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| unitLabel: 'Grad', snapWidth: 5
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| }),
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| sldT = cnfBox.create('slider', [ [-0.7, -1.5], [3, -1.5], [0, 0, 10] ], {
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| suffixlabel: '$t=$',
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| unitLabel: 's', snapWidth: 0.2
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| }),
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| // Definition der Funktion
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| signaldarstellung = pltBox.create('functiongraph', [function(x) {
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| return (sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * x - 2 * Math.PI * sldPHI1.Value() / 360) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * x - 2 * Math.PI * sldPHI2.Value() / 360))
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| }], {
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| strokeColor: "red"
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| });
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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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| p_T0 = pltBox.create('point', [
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| function() {
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| return (Math.round(getT0() * 100) / 100);
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| },
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| function() {
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| return sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI1.Value() / 360) +
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| sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI2.Value() / 360);
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| }],
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| { color: "blue", fixed: true, label: false, size: 1, name: '' }
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| );
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| p_T0h = pltBox.create('point',
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| [function() { return (Math.round(getT0() * 100) / 100); }, 2],
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| { visible: false, color: "blue", fixed: true, label: false, size: 1, name: '' }
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| );
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| l_T0 = pltBox.create('line', [p_T0, p_T0h])
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| // Bestimmung des Wertes T_0 mit der Funktion von Siebenwirth
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| setInterval(function() {
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| document.getElementById("T_0").innerHTML = Math.round(getT0() * 100) / 100;
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| }, 50);
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| function isInt(n) {
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| return n % 1 === 0;
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| }
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| function getT0() {
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| var A, B, C, Q;
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| if (sldF1.Value() < sldF2.Value()) {
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| A = sldF1.Value();
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| B = sldF2.Value();
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| } else {
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| B = sldF1.Value();
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| A = sldF2.Value();
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| }
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| // console.log('Berechne T0 mit A=' + A, 'B=' + B);
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| for (var x = 1; x <= 100; x++) {
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| C = A / x;
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| Q = B / C;
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| // console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q);
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| if (isInt(Q)) {
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| // console.log('Q ist eine Ganzzahl!!! T0 ist damit ', 1 / C);
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| return 1 / C;
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| }
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| if (x === 10) {
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| return 10;
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| }
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| if ((1 / C) > 10)
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| return 10
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| }
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| }
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| // Ausgabe des Wertes x(t)
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| setInterval(function() {
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| document.getElementById("x(t)").innerHTML = Math.round((sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * sldT.Value() - 2 * Math.PI * sldPHI1.Value() / 360) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * sldT.Value() - 2 * Math.PI * sldPHI2.Value() /
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| 360)) * 1000) / 1000;
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| }, 50);
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| // Ausgabe des Wertes x(t+T_0)
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| setInterval(function() {
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| document.getElementById("x(t+T_0)").innerHTML = Math.round((sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (sldT.Value() + Math.round(getT0() * 1000) / 1000) - sldPHI1.Value()) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (sldT.Value() +
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| Math.round(getT0() * 1000) / 1000) - sldPHI2.Value())) * 1000) / 1000;
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| }, 50);
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| // Ausgabe des Wertes x(t+2T_0)
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| setInterval(function() {
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| document.getElementById("x(t+2T_0)").innerHTML = Math.round((sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (sldT.Value() + 2 * Math.round(getT0() * 1000) / 1000) - sldPHI1.Value()) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (sldT.Value() +
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| 2 * Math.round(getT0() * 1000) / 1000) - sldPHI2.Value())) * 1000) / 1000;
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| }, 50);
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| // Ausgabe des Wertes x_max
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| setInterval(function() {
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| var x = new Array(50000);
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| for (var i = 0; i < 50001; i++) {
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| x[i] = Math.round((sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (i / 1000) - 2 * Math.PI * sldPHI1.Value() / 360) + sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (i / 1000) - 2 * Math.PI * sldPHI2.Value() / 360)) * 1000) / 1000;
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| }
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| document.getElementById("x_max").innerHTML = Math.max.apply(Math, x);
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| }, 50);
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| };
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| // Definition der Funktion zum An- und Ausschalten des Koordinatengitters
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| function showgrid() {
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| if (gridbox.checked) {
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| xaxis = pltBox.create('axis', [ [0, 0], [1, 0] ], {});
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| yaxis = pltBox.create('axis', [ [0, 0], [0, 1] ], {});
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| } else {
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| xaxis.removeTicks(xaxis.defaultTicks);
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| yaxis.removeTicks(yaxis.defaultTicks);
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| }
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| pltBox.fullUpdate();
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| };
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| </script>
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| </body>
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| </html>
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| {{Display}}
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