Question

A particle is in its state of uniform circular motion. prove that its projection along one of its diameter executes simple harmonic motion.

Answer 1

The displacement of the projection along the diameter from the Center of the circle is given by :-

x = R Cos wt, if x = R at t = 0

Uniform circular motion means

that w is a constant.

Then v = dx/dt = Rw Sinwt

a = d²x/dt² = - Rw² Cos wt = -w² x

Hence its motion is a SHM