HelmutKnaust: Created page with "Below are the time series and the phase portrait for a harmonic oscillator, subject to a the second-order linear differential equation of the form \[y''(t)+p y'(t)+4 y(t)=0.\]..."

2013-10-29T16:54:26Z

Created page with "Below are the time series and the phase portrait for a harmonic oscillator, subject to a the second-order linear differential equation of the form \[y''(t)+p y'(t)+4 y(t)=0.\]..."

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Below are the time series and the phase portrait for a harmonic oscillator, subject to a the second-order linear differential equation of the form
\[y''(t)+p y'(t)+4 y(t)=0.\]

The oscillator is critically damped when $p=4$. The graphs are depicted in red when the spring is underdamped (or undamped), green when the spring is critically damped, and blue in the overdamped case.

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<script type="text/javascript">
var cdf = new cdfplugin();
cdf.embed('http://helmut.knaust.info/Demos/Spring1.cdf', 692, 553);
</script>
</html>

Note below that the critically damped case features one pair of straight-line solutions. That pair splits into two pairs of straight-line solutions when the oscillator becomes overdamped.

You can move the "cross-hair" locator to see a different solution.

<html>
<script type="text/javascript" src="http://www.wolfram.com/cdf-player/plugin/v2.1/cdfplugin.js"></script>
<script type="text/javascript">
var cdf = new cdfplugin();
cdf.embed('http://helmut.knaust.info/Demos/Spring2.cdf', 592, 680);
</script>
</html>

Demonstration: Harmonic Oscillator - Revision history

HelmutKnaust: Created page with "Below are the time series and the phase portrait for a harmonic oscillator, subject to a the second-order linear differential equation of the form \[y''(t)+p y'(t)+4 y(t)=0.\]..."