Simulating a Water Wave Using a Cycloid

This Demonstration shows a curtate cycloid, a figure traced by a fixed point in the interior of a rolling circle.

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DETAILS

A cycloid has parametric equations:
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To simulate a wave, the parameter is inverted. The actual equations used in this Demonstration are:
,
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The term corresponds to the wave height. Almost all Demonstrations of cycloids incorporate the rolling circle for effect. With a little effort, it was possible to show that effect (along with basic wave parameters) by tweaking the original parametric equations.
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