Solve Spring SHM Problem: Period of Oscillation in M1, M2, k

[brendan3eb]

Homework Statement

Two blocks of mass M2 and M1 (M2>M1) are connected by a spring with force constant k and are free to slide on a frictionless table. They are pulled apart and then released from rest. In terms of M1, M2, and k, what would the period of oscillation be?

Homework Equations

T=2PI*sqrt(m/k)
f=-kx

The Attempt at a Solution

So taking the starting position to be both blocks just before they released, one full cycle would be when they have both returned to their initial positions. Other than noting this, the problem leaves me perplexed as to what to do next..all I need is a hint in the right direction. I guess just picturing such an apparatus in my head is mind-boggling. Would the equilibrium point remain the same or would it start to expand and contract abnormally?

 

[Shooting Star]

The CM wouldn't move, so you could start by taking that as the origin. Take x1 and x2 to be the positions of the masses etc. Now, write the force eqns on the springs. Take x=x1-x2, the dist between the two springs.

Your aim is to only find the w. Once you have reduced the two eqns to a form of Mx'' = -k'x, for some M, then directly you can find w. A bit of algebraic manipulation is reqd.