A 0.50kg block attached to a horizontal spring executes simple harmonic motion on a smooth surface. At t=0, the block is 0.15m to the right of the equilibrium position and moving toward the equilibrium position with a speed of 0.50ms−1. The force constant of the spring is 40Nm−1.
(a) Derive the expression for the displacement x(t) of the block for subsequent times.
(b) Using the expression obtained in part (a), determine the earliest time t>0 at which the kinetic energy of the block becomes three times its potential energy.