Cycloidal pendulum 
This applet illustrates the possibility of obtaining a pendulum with a frequency that does not depend on the amplitude of the oscillations i.e., is constant, even for large amplitudes. This is achieved by placing a «constraining » curve for the pendulum string, which causes the usable length of the pendulum to decrease as the amplitude increases. By choosing an adequate shape for this curve, it is possible to ensure that the (opposite) effects of these variations (greater initial amplitude -> greater period and smaller length -> smaller period) are exactly compensated. It is proved that the solution is a cycloid and the applet allows experimentally verifying said independence.
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