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The cycloid is the evolute of an identical cycloid
.
This means that if a thread supporting a weight is forced to move
along a cycloid, then the weight
supported by the thread describes another cycloid.
However, because the time a body
takes to reach point A on the cycloid is independent from its starting point,
(tautochron curve ),it follows that the period
of suspension is independent from the amplitude of oscillation.
The exhibit shows the difference between a cycloidal pendulum,
which is perfectly isochronic, and an ordinary pendulum.
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