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 ( Atilde sin Atilde ), y a (cos Atilde 1) Where the length of the pendulum is l 4a, and where Atilde is the angle of rotation of the circle ...

The force responsible for the motion of the pendulum bob is the component of the gravitational forc ...

A pendulum is suspended from the cusp of a cycloid* cut in a rigid support (Figure 3-A).

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 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.

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