Oscillating block on a spring: At which moment is K=U?

Question

Consider a harmonic oscillator at four different moments, labeled A, B, C, and D, as shown in the figure http://session.masteringphysics.com/problemAsset/1003620/23/1003620.jpg .

Assume that the force constant k, the mass of the block, m, and the amplitude of vibrations, A, are given. Assume that there are no resistive forces; that is, E=constant

At which moment is K=U?

Choose from A-D and explain why

Answer 1

The answer is D. There is some mathematical work needed to be done to show this. I will let you play with the equations for the kinetic and potential energy of the block and the spring at point D using the fact that it is at -A*sqrt(2) / 2. In general though, K = U at this point because half of the energy is potential and the other half is kinetic. Logically this makes sense since the point D is between the two extremes which are at the equilibrium point and the endpoint -A. You already know how the kinetic and potential energies correspond to these two points and compare with each other so this should make sense to you logically that half of the energy is kinetic and half is potential which is why K = U at this point.