|
|
| Zeile 1: |
Zeile 1: |
| | + | {{LntAppletLink|periode}} |
| | + | Dieses Applet beschreibt ... |
| | | | |
| | <p> | | <p> |
| Zeile 7: |
Zeile 9: |
| | </p> | | </p> |
| | | | |
| − | <html>
| + | {{LntAppletLink|periode}} |
| − | <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://www.lntwww.de/MathJax/unpacked/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full,local/mwMathJaxConfig"></script> -->
| |
| − | <!-- <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML-full"></script> -->
| |
| − | <style>
| |
| − | .wrapper1{
| |
| − | display:grid;
| |
| − | grid-row-gap:1em;
| |
| − | justify-items:stretch;
| |
| − | align-items:stretch;
| |
| − | }
| |
| − | | |
| − | .wrapper1 >div{
| |
| − | padding:0em;
| |
| − | | |
| − | }
| |
| − | .wrapper1 >div:nth-child(odd){
| |
| − | }
| |
| − | .wrapper2{
| |
| − | display:grid;
| |
| − | grid-row-gap:1em;
| |
| − | grid-template-columns:70% 30%;
| |
| − | justify-items:stretch;
| |
| − | align-items:stretch;
| |
| − | | |
| − | }
| |
| − | | |
| − | .wrapper2 >div{
| |
| − | padding:0em;
| |
| − | | |
| − | grid-template-columns:repeat(2);}
| |
| − | | |
| − | | |
| − | .box4{
| |
| − | grid-column:1/3;
| |
| − | grid-row:4/4;
| |
| − | border: 1px solid black;
| |
| − | }
| |
| − | .box5{
| |
| − | grid-column:2/3;
| |
| − | grid-row:4/4;
| |
| − | border: 1px solid black;
| |
| − | }
| |
| − | | |
| − | .button {
| |
| − | background-color: black;
| |
| − | border: none;
| |
| − | color: white;
| |
| − | font-family: arial;
| |
| − | padding: 8px 20px;
| |
| − | text-align: center;
| |
| − | text-decoration: none;
| |
| − | display: inline-block;
| |
| − | font-size: 16px;
| |
| − | border-radius: 15px;
| |
| − | }
| |
| − | .button:active {
| |
| − | background-color: #939393;
| |
| − | }
| |
| − | </style>
| |
| − | </head>
| |
| − | | |
| − | <body onload="drawNow()">
| |
| − | <!-- Resetbutton, Checkbox und Formel -->
| |
| − | | |
| − | <div class="wrapper1">
| |
| − | <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:150px; "></div>
| |
| − | <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black;"></div>
| |
| − | </div>
| |
| − | | |
| − | <!-- Ausgabefelder -->
| |
| − | | |
| − | <div class="wrapper2">
| |
| − | | |
| − | <div>
| |
| − | <table>
| |
| − | <tr>
| |
| − | <td>$x(t)$= <span id="x(t)"></span> $\quad$ </td>
| |
| − | <td>$x(t+ T_0)$= <span id="x(t+T_0)"></span> $\quad$ </td>
| |
| − | <td>$x(t+2T_0)$= <span id="x(t+2T_0)"></span> $\quad$ </td>
| |
| − | <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>
| |
| − | </table>
| |
| − | </div>
| |
| − | | |
| − | <div>
| |
| − | | |
| − | <p>
| |
| − | <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien zeigen</label>
| |
| − | <button class="button" onclick="drawNow();">Reset</button>
| |
| − | </p>
| |
| − | | |
| − | </div>
| |
| − | </div>
| |
| − | | |
| − | | |
| − | <script type="text/javascript">
| |
| − | function drawNow() {
| |
| − | // Grundeinstellungen der beiden Applets
| |
| − | JXG.Options.text.useMathJax = true;
| |
| − | 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]
| |
| − | });
| |
| − | 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
| |
| − | xaxis = pltBox.create('axis', [[0, 0], [1, 0]], {
| |
| − | name: '$\\dfrac{t}{T}$',
| |
| − | 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
| |
| − | sldA1 = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], {
| |
| − | suffixlabel: '$A_1=$',
| |
| − | unitLabel: 'V', snapWidth: 0.01
| |
| − | }),
| |
| − | sldF1 = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], {
| |
| − | suffixlabel: '$f_1=$',
| |
| − | unitLabel: 'kHz', snapWidth: 0.1
| |
| − | }),
| |
| − | sldPHI1 = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], {
| |
| − | suffixlabel: '$\\phi_1=$',
| |
| − | unitLabel: 'Grad', snapWidth: 5
| |
| − | }),
| |
| − | sldA2 = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], {
| |
| − | suffixlabel: '$A_2=$',
| |
| − | unitLabel: 'V', snapWidth: 0.01
| |
| − | }),
| |
| − | sldF2 = cnfBox.create('slider', [ [6, 0.5], [9.7, 0.5], [0, 2, 10] ], {
| |
| − | suffixlabel: '$f_2=$',
| |
| − | unitLabel: 'kHz', snapWidth: 0.1
| |
| − | }),
| |
| − | sldPHI2 = cnfBox.create('slider', [ [6, -0.5], [9.7, -0.5], [-180, 90, 180] ], {
| |
| − | suffixlabel: '$\\phi_2=$',
| |
| − | unitLabel: 'Grad', snapWidth: 5
| |
| − | }),
| |
| − | sldT = cnfBox.create('slider', [ [-0.7, -1.5], [3, -1.5], [0, 0, 10] ], {
| |
| − | suffixlabel: '$t=$',
| |
| − | unitLabel: 's', snapWidth: 0.2
| |
| − | }),
| |
| − | // Definition der Funktion
| |
| − | signaldarstellung = pltBox.create('functiongraph', [function(x) {
| |
| − | 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))
| |
| − | }], {
| |
| − | strokeColor: "red"
| |
| − | });
| |
| − | // 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 sldA1.Value() * Math.cos(2 * Math.PI * sldF1.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI1.Value() / 360) +
| |
| − | sldA2.Value() * Math.cos(2 * Math.PI * sldF2.Value() * (Math.round(getT0() * 100) / 100) - 2 * Math.PI * sldPHI2.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
| |
| − | setInterval(function() {
| |
| − | document.getElementById("T_0").innerHTML = Math.round(getT0() * 100) / 100;
| |
| − | }, 50);
| |
| − | function isInt(n) {
| |
| − | return n % 1 === 0;
| |
| − | }
| |
| − | function getT0() {
| |
| − | var A, B, C, Q;
| |
| − | if (sldF1.Value() < sldF2.Value()) {
| |
| − | A = sldF1.Value();
| |
| − | B = sldF2.Value();
| |
| − | } else {
| |
| − | B = sldF1.Value();
| |
| − | A = sldF2.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 Ganzzahl!!! T0 ist damit ', 1 / C);
| |
| − | return 1 / C;
| |
| − | }
| |
| − | if (x === 10) {
| |
| − | return 10;
| |
| − | }
| |
| − | if ((1 / C) > 10)
| |
| − | return 10
| |
| − | }
| |
| − | }
| |
| − | // Ausgabe des Wertes x(t)
| |
| − | setInterval(function() {
| |
| − | 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() /
| |
| − | 360)) * 1000) / 1000;
| |
| − | }, 50);
| |
| − | // Ausgabe des Wertes x(t+T_0)
| |
| − | setInterval(function() {
| |
| − | 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() +
| |
| − | Math.round(getT0() * 1000) / 1000) - sldPHI2.Value())) * 1000) / 1000;
| |
| − | }, 50);
| |
| − | // Ausgabe des Wertes x(t+2T_0)
| |
| − | setInterval(function() {
| |
| − | 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() +
| |
| − | 2 * Math.round(getT0() * 1000) / 1000) - sldPHI2.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((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;
| |
| − | }
| |
| − | 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();
| |
| − | };
| |
| − | </script>
| |
| − | </body>
| |
| − | </html>
| |
| − | | |
| − | {{Display}}
| |
