Which moment corresponds to the minimum kinetic energy of the system?

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.

Which moment corresponds to the minimum kinetic energy of the system?

A B C or D and why?

I tried C, why is C wrong?

Answer 1

A and D... remember potential energy is expressed by u=0.5*k*(x^2)..since K is a constant,and X is max at both tips (A and D),so potential energy is maximum, and according to the law of conservation of energy,that would be the point at which Kinetic Energy is minimum.....

Answer 2

C seems right to me.

Edit: d**n i should read.... C is the maximum.

It would be A.

Minimum kinetic energy is where the mass has stopped moving, and at full amplitude all the kinetic is stored as potential... therefore no kinetic energy.

Answer 3

The answer is A.

When the block is displaced a distance A from equilibrium, the spring is stretched (or compressed) the most, and the block is momentarily at rest. Therefore, the maximum potential energy is U_max = (1/2)kA^2. At that moment, of course, K = K_min = 0. Recall that E = K + U. Therefore,

E = (1/2)kA^2

In general, the mechanical energy of a harmonic oscillator equals its potential energy at the maximum or minimum displacement.

So, C is wrong because C corresponds to the maximum kinetic energy of the system. The guy above me is wrong in saying that it is both A and D because the spring oscillates back and forth between A and -A, and D is not at point -A it is at -A*sqrt(2) / 2 which is not an 'endpoint' so to speak. If D were at -A then he would be correct, but it's not. Therefore, the answer is A ONLY.

Answer 4

In drawing C, the oscillator is at equilibrum position. Its potential energy is 0 and its kinetic energy maximum

In drawing A, the oscillator is at border position. Its potential energy is maximuum and its kinetic energy is 0

The answer should be A