Difference between revisions of "Applets:Periodendauer periodischer Signale"
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<html> | <html> | ||
<head> | <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://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> | <script type="text/javascript" src="https://cdn.rawgit.com/mathjax/MathJax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> | ||
− | + | <style> | |
− | + | .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; | |
− | + | } | |
− | + | table { | |
− | + | border-collapse: separate; | |
− | + | border-spacing: 20px 0; | |
− | + | } | |
− | + | </style> | |
</head> | </head> | ||
− | |||
− | <form id=" | + | <body> |
− | + | <form id="jxgForm"> | |
− | <!-- Resetbutton, Checkbox und | + | <!-- Resetbutton, Checkbox, Regler und Plots --> |
− | < | + | <p> |
− | <p>< | + | <input type="checkbox" id="gridbox" onclick="showgrid();" checked> <label for="gridbox">Gitterlinien zeigen</label> |
+ | <button class="button" onclick="rst()">Reset</button> | ||
+ | </p> | ||
+ | <div id="cnfBoxHtml" class="jxgbox" style="width:600px; height:100px; float:top; margin:-10px 20px 100px 0px;"></div> | ||
+ | <div id="pltBoxHtml" class="jxgbox" style="width:600px; height:600px; border:1px solid black; margin:-10px 20px 100px 0px;"></div> | ||
+ | </form> | ||
+ | <!-- Ausgabefelder --> | ||
+ | <table> | ||
+ | <tr> | ||
+ | <td>$x(t)$= <span id="x(t)"></span> </td> | ||
+ | <td>$x(t+ T_0)$=<span id="x(t+T_0)"></span> </td> | ||
+ | <td>$x(t+2T_0)$=<span id="x(t+2T_0)"></span></td> | ||
+ | </tr> | ||
+ | <tr> | ||
+ | <td>$x_{\text{max}}$=<span id="x_max"></span></td> | ||
+ | <td>$T_0$= <span id="T_0"></span> </td> | ||
+ | </tr> | ||
+ | </table> | ||
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<script type="text/javascript"> | <script type="text/javascript"> | ||
+ | // Grundeinstellungen der beiden Applets | ||
+ | JXG.Options.text.useMathJax = true; | ||
+ | var 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] | ||
+ | }); | ||
+ | var 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 |
− | + | a = cnfBox.create('slider', [ [-0.7, 1.5], [3, 1.5], [0, 0.5, 1] ], { | |
− | + | suffixlabel: '$A_1=$', | |
+ | unitLabel: 'V', snapWidth: 0.01 | ||
+ | }), | ||
+ | b = cnfBox.create('slider', [ [-0.7, 0.5], [3, 0.5], [0, 1, 10] ], { | ||
+ | suffixlabel: '$f_1=$', | ||
+ | unitLabel: 'kHz', snapWidth: 0.1 | ||
+ | }), | ||
+ | c = cnfBox.create('slider', [ [-0.7, -0.5], [3, -0.5], [-180, 0, 180] ], { | ||
+ | suffixlabel: '$\\phi_1=$', | ||
+ | unitLabel: 'Grad', snapWidth: 5 | ||
+ | }), | ||
+ | d = cnfBox.create('slider', [ [6, 1.5], [9.7, 1.5], [0, 0.5, 1] ], { | ||
+ | suffixlabel: '$A_2=$', | ||
+ | unitLabel: 'V', snapWidth: 0.01 | ||
+ | }), | ||
+ | e = cnfBox.create('slider', [ [6, 0.5], [9.7, 0.5], [0, 2, 10] ], { | ||
+ | suffixlabel: '$f_2=$', | ||
+ | unitLabel: 'kHz', snapWidth: 0.1 | ||
+ | }), | ||
+ | g = cnfBox.create('slider', [ [6, -0.5], [9.7, -0.5], [-180, 90, 180] ], { | ||
+ | suffixlabel: '$\\phi_2=$', | ||
+ | unitLabel: 'Grad', snapWidth: 5 | ||
+ | }), | ||
+ | t = 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) { | |
− | b | + | 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)) |
− | c | + | }], { |
− | d | + | strokeColor: "red" |
− | e | + | }); |
− | g | ||
− | |||
+ | // 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 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 = 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); | |
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− | + | function isInt(n) { | |
− | + | return n % 1 === 0; | |
− | + | } | |
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function getT0() { | function getT0() { | ||
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var A, B, C, Q; | var A, B, C, Q; | ||
if (b.Value() < e.Value()) { | if (b.Value() < e.Value()) { | ||
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A = e.Value(); | A = e.Value(); | ||
} | } | ||
− | + | // console.log('Berechne T0 mit A=' + A, 'B=' + B); | |
− | console.log('Berechne T0 mit A=' + A, 'B=' + B); | ||
− | |||
for (var x = 1; x <= 100; x++) { | for (var x = 1; x <= 100; x++) { | ||
C = A / x; | C = A / x; | ||
Q = B / C; | Q = B / C; | ||
− | console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q); | + | // console.log(x + '. Durchgang: C = ' + C, 'Q = ' + Q); |
if (isInt(Q)) { | if (isInt(Q)) { | ||
− | console.log('Q ist eine | + | // console.log('Q ist eine Ganzzahl!!! T0 ist damit ', 1 / C); |
return 1 / C; | return 1 / C; | ||
} | } | ||
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return 10; | return 10; | ||
} | } | ||
− | if ((1/C) > 10) | + | if ((1 / C) > 10) |
return 10 | return 10 | ||
} | } | ||
} | } | ||
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+ | |||
+ | // 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; | ||
+ | }, 50); | ||
+ | |||
+ | // 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; | ||
+ | }, 50); | ||
+ | |||
+ | // Ausgabe des Wertes x(t+2T_0) | ||
+ | setInterval(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; | ||
+ | }, 50); | ||
+ | |||
+ | // Ausgabe des Wertes x_max | ||
+ | setInterval(function() { | ||
+ | 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); | ||
+ | }, 50); | ||
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− | + | // 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(); | ||
+ | }; | ||
− | //Definition des Reset-Buttons | + | // Definition des Reset-Buttons |
− | function | + | function rst() { |
− | + | document.getElementById("jxgForm").reset(); | |
− | }; | + | }; |
</script> | </script> | ||
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</body> | </body> | ||
</html> | </html> | ||
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− |
Revision as of 17:10, 13 September 2017
$x(t)$= | $x(t+ T_0)$= | $x(t+2T_0)$= |
$x_{\text{max}}$= | $T_0$= |