Aliasing in Pendulum Waves

This Demonstration simulates pendulum waves with 10 to 20 uncoupled pendulums and a period of 30 to 90 seconds. The linear approximation to pendulum motion is used, so that larger angles are less accurately represented. The dots represent individual pendulums viewed from above. The light gray line plotted underneath is an approximation of the waveform. The Demonstration shows how aliasing produces the visual effects in the pendulum waves as seen in [1] and [2]. Aliasing in signal processing relates to the relationship between analog data and its approximation in digital form.
For best results, slow the step speed until the time variable is about 1 unit/second.


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For more information on simple harmonic and non-harmonic motion, see [1].
[1] Harvard Natural Sciences Lecture Demonstrations, "Simple Harmonic (and Non-Harmonic) Motion."
[2] R. E. Berg, "Pendulum Waves: A Demonstration of Wave Motion Using Pendula," American Journal of Physics, 59(2), 1991 pp. 186–187.
[3] J. A. Flaten and K. A. Parendo, "Pendulum Waves: A Lesson in Aliasing," American Journal of Physics, 69(7), 2001 pp. 778–782.
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