How Does Spring Compression Affect Power Transfer to a Moving Ladle?

[Predator]

Homework Statement

A 0.33 kg ladle sliding on a horizontal frictionless surface is attached to one end of a horizontal spring (with k = 485 N/m) whose other end is fixed. The mass has a kinetic energy of 10 J as it passes through its equilibrium position (the point at which the spring force is zero).
(a) At what rate is the spring doing work on the ladle as the ladle passes through its equilibrium position?

(b) At what rate is the spring doing work on the ladle when the spring is compressed 0.10 m and the ladle is moving away from the equilibrium position?

Homework Equations

W = KE(final) - KE(initial)

W = 1/2kx^2

The Attempt at a Solution

Ok, on A, I kinda had to use intuition and guess that when the ladle passes through the equilbrium position, the force is 0, thus the work is 0. Then, that causes me to come to a problem at B, I do not understand how to solve it. I'm guessing I need Force * velocity...and it says that the KE @ equilibrum = 10J, so how do I use that to get V? (K = 1/2mv^2)

 

[Shooting Star]

The total energy, ke+pe, is constant and is given in the problem. It is 10 J. So you know k. From that, find v at 0.10m. The rate of work done is –Fv at a point. F is known for any x.