Calculating Energy of Two Masses on a Spring

[bessletama]

Homework Statement

Consider the following macroscopic oscillator: Two masses of equal mass are attached to a spring and oscillate with amplitude A at frequency v. Use classical physics to calculate the energy of the oscillator.

Homework Equations

The Attempt at a Solution

This question doesn't say much about where the mass is attached or what environment this oscillator is in so I assumed that we're in a friction-less environment and the mass is attached on either end of the spring. Please tell me if that is incorrect.
Based on that assumption, I know that the position of one of the mass would travel in a cosine curve. So we have p(t)=A*cos(2*pi*v*x). I can take the derivative of this to get the velocity v(t)=-2*pi*A*v*sin(2*pi*v*x). The maximum velocity is when t=1/(4v). Let's call this new velocity V. Now the energy of the spring should be 2*((1/2)*m*V^2). Is this correct? Or is there another way to do it.

Thanks in advance!

 

[Simon Bridge]

I assumed that we're in a friction-less environment and the mass is attached on either end of the spring. Please tell me if that is incorrect.

You should verify the assumption ... but it is what I'd do.

What you seem to have done is considered the motion of just one mass, assuming the other one is stationary.

The force on the masses depends on their relative positions - so you'd work out the free body diagram and solve the resulting differential equation.

If their motion is antisymmetric with the same amplitude, then you can simplify the problem quite a lot.