A block of mass m oscillates horizontally on a frictionless surface, attached to an ideal spring with equilibrium position at x=0. The block is released from rest at x=+A and moves with simple harmonic motion of period T. At various later instants the student records the mechanical energy that is kinetic, K, and the energy stored elastically in the spring, U. Assume no non-conservative forces act.
(a) Describe qualitatively how the fraction K/Etotal varies as the block moves from x=0 out to x=+A and then back through x=0 to x=−A. In your description, refer explicitly to the values of the fraction at the extreme points and at the equilibrium point.
(b) Explain, using energy conservation, why K and U cannot both be simultaneously maximal or both be simultaneously minimal at any point in the motion.
(c) Suppose the student claims that the kinetic energy equals one–half of the total mechanical energy when the displacement is x=21A. Evaluate this claim and justify your reasoning based on the functional dependence of each type of energy on displacement.