A body of mass m attached to a horizontal spring performs simple harmonic motion of amplitude A along the x-axis. It is released from rest at x=+A at t=0.
a) Derive a general expression for the time tn at which the body crosses a particular displacement x(0<x<A) for the n-th time after the start.
b) Using your result, obtain an expression for the time interval between the 3rd and the 7th crossings of the same displacement x.
c) Evaluate this interval numerically for x=0.20A and ω=4rads−1.