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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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| − | }}
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| − | </p>
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| − |
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| − | <html>
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| − | <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://www.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> | | <style> |
| − | .button {
| + | body { |
| − | background-color: black;
| + | font-family: sans-serif; |
| − | border: none;
| + | font-size: 0.875em; |
| − | 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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| − | | |
| − | .grid {
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| − | display: grid;
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| − | grid-template-columns: 70% 30%;
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| − | grid-gap: 10px;
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| | } | | } |
| − | | + | .container { |
| − | .box:nth-child(3), | + | top: 20px; |
| − | .box:nth-child(4)
| + | left: 20px; |
| − | {
| + | width: 400px; |
| − | grid-column: span 2; | + | height: 300px; |
| − | } | + | border-style: dotted; |
| − | | + | border-width: 1px; |
| − | </style>
| + | padding: 20px; |
| − | </head>
| + | } |
| − | | + | .blue { |
| − | <body onload="drawNow()">
| + | background-color: #ccccff; |
| − | | + | } |
| − | <div class="grid">
| + | .green { |
| − | | + | background-color: #ccffcc; |
| − | <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px; float:top; margin:-10px 20px 100px 0px;"></div>
| + | } |
| − | | + | </style> |
| − | <div>
| + | <script> |
| − | <p>
| + | // Create PanelLayouts to add to the GridLayout. |
| − | <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien Zeigen</label>
| + | var panel1 = new OO.ui.PanelLayout( { |
| − | <button class="button" onclick="drawNow();">Reset</button>
| + | $content: $( '<p>Panel One</p>'), |
| − | </p>
| + | classes: ['blue'] |
| − | </div>
| + | }); |
| − | | + | |
| − | <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-100px 20px 10px 0px;"></div>
| + | var panel2 = new OO.ui.PanelLayout( { |
| − | | + | $content: $( '<p>Panel Two</p>' ), |
| − | <div>
| + | classes: ['green'] |
| − | <table>
| + | }); |
| − | <tr>
| + | |
| − | <td>$x(t)$= <span id="x(t)"></span> $\quad$ </td>
| + | var panel3 = new OO.ui.PanelLayout( { |
| − | <td>$x(t+ T_0)$= <span id="x(t+T_0)"></span> $\quad$ </td>
| + | $content: $( '<nowiki><p>Panel Three</p>' ), |
| − | <td>$x(t+2T_0)$= <span id="x(t+2T_0)"></span> $\quad$ </td>
| + | classes: ['green'] |
| − | <td>$x_{\text{max}}$= <span id="x_max"></span> $\quad$ </td>
| + | }); |
| − | <td style="color:blue;">$T_0$= <span id="T_0"></span> $\quad$ </td>
| + | |
| − | </tr>
| + | var panel4 = new OO.ui.PanelLayout( { |
| − | </table> | + | $content: $( '<nowiki><p>Panel Four</p>' ), |
| − | </div>
| + | classes: ['blue'] |
| − | | + | }); |
| − | </div>
| + | |
| − | | + | // Create a GridLayout. |
| − | | + | var grid = new OO.ui.GridLayout( [ panel1, panel2, panel3, panel4 ], { |
| − | | + | classes: [ 'container' ], |
| − | <script type="text/javascript"> | + | widths: [ 1/2 , 1/2 ], |
| − | function drawNow() {
| + | heights: [ 1/2 , 1/2 ] |
| − | // Grundeinstellungen der beiden Applets
| + | } ); |
| − | JXG.Options.text.useMathJax = true;
| + | $( 'body' ).append( grid.$element ); |
| − | 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> | | </script> |
| − | </body>
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| − | </html>
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| − |
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| − | {{Display}}
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