A particle executes simple harmonic motion of amplitude A and angular frequency ω along a straight line. At t=0s it is released from the positive extreme position.
a) Explain, with suitable reasoning, why the instants at which the particle passes through a fixed displacement x (where 0<x<A) repeat at regular intervals.
b) Determine what this interval equals in terms of the time period T of the oscillation.
c) How many distinct times (counting motion in both directions) does the particle cross the displacement x during one complete oscillation?