What is the Amplitude of a Mass-Spring System?

[dukkie]

A block of mass 0.25 kg is connected to a spring with a spring constant (k) of 35 N/m. It is oscillating on a frictionless horizontal surface. It's speed as it passes through equilibrium is 1.04 m/s. What is the total energy of the system?

I know that E=0.5(k)(A)^2. I just can't figure out the Amplitude. I know I can do it. I just don't know what kind of equation to use to get the amplitude. I have tried using x=A cos (wt) but that wasn't right. I have also tried vmax=A(k/m), that wasn't right either. I'm confused.

 

[Fermat]

Since the body is connected to only one spring (if it was oscillating while attached to two springs which were both under compression at all times, then that would be different) then there is no compression or extension in the spring at the equilibrium point, hence there is no potential energy in the spring at that point.
All the energy is therefore just kinetic energy. You have the mass and the velocity at the equilibrium point, so you can find the KE.

 

[dukkie]

Thanks so much for your help. I miss the most simple solutions sometimes. It helped a lot for you to explain it. Thanks again. I got it right.