Applets:Periodendauer periodischer Signale: Unterschied zwischen den Versionen
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+ | <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> | ||
+ | <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}} |
Version vom 20. September 2017, 16:00 Uhr
Funktion: $$x(t) = A_1\cdot cos\Big(2\pi f_1\cdot t- \frac{2\pi}{360}\cdot \phi_1\Big)+A_2\cdot cos\Big(2\pi f_2\cdot t- \frac{2\pi}{360}\cdot \phi_2\Big)$$
$x(t)$= $\quad$ | $x(t+ T_0)$= $\quad$ | $x(t+2T_0)$= $\quad$ | $x_{\text{max}}$= $\quad$ | $T_0$= $\quad$ |