Consider a block–spring system executing simple harmonic motion of amplitude A and angular frequency ω on a smooth horizontal track. The block is at the extreme right position (x=+A) at time t=0.
(a) Show that the work done by the spring force during the subsequent motion of the block from t=0 to the instant when the block first reaches the mean position is equal in magnitude to the total mechanical energy of the system.
(b) Calculate the average rate at which this work is performed (average power of the spring force) during this interval.
(c) Comment on whether the average power of the spring force over one complete oscillation is positive, negative or zero, and justify your answer.