Question: A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is

A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A). The path described by the pendulum bob is cycloidal and is given by x = a (Ã˜ - sin Ã˜), y = a (cos Ã˜ €“ 1)
Where the length of the pendulum is l = 4a, and where Ã˜ is the angle of rotation of the circle generating the cycloid. Show that the oscillations are exactly isochronous with frequency w0 = √g / l, independent of the amplitude.

2a 2a

2a 2a

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