Consider a block of mass m attached to a spring with force constant k.After the block is released, it will..?

Question

Consider a block of mass m attached to a spring with force constant k, as shown in the figure http://session.masteringphysics.com/problemAsset/1003614/20/168450A.jpg . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

After the block is released from x=A, it will

A: remain at rest.

B: move to the left until it reaches equilibrium and stop there.

C: move to the left until it reaches x=-A and stop there.

D: move to the left until it reaches x=-A and then begin to move to the right.

Make a selection from A, B, C, or D and explain your reasoning why.

Answer 1

"The block slides on a frictionless horizontal surface, as shown."

So you have no friction

"Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block."

and there is no damping going on with the spring

"If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations."

The question answers itself.

Answer 2

the answer is D

As the block begins its motion to the left, it accelerates. Although the restoring force decreases as the block approaches equilibrium, it still pulls the block to the left, so by the time the equilibrium position is reached, the block has gained some speed. It will, therefore, pass the equilibrium position and keep moving, compressing the spring. The spring will now be pushing the block to the right, and the block will slow down, temporarily coming to rest at x = -A.

After x = -A is reached, the block will begin its motion to the right, pushed by the spring. The block will pass the equilibrium position and continue until it reaches x = A, completing one cycle of motion. The motion will then repeat; if, as we've assumed, there is no friction, the motion will repeat indefinitely.

Answer 3

D, because the amplitude is said to be a, so if it is A units up, it will go to A units past the rest point.  Plus it has to go back, (oscillation)