Coupled oscillators and normal modes question

[warfreak131]

Homework Statement

Two equal masses are held on a frictionless track by 3 equal springs, attached to two rigid posts. If either of the masses is clamped, the period (t=2pi/w) of one oscillation is three seconds.

If both masses are free, what is the periods of oscillation of both normal modes?

Homework Equations

The Attempt at a Solution

We learned in class that one fixed mass resulted in w=sqrt(2k/m), both traveling in the same direction with equal distance between them results in w=sqrt(k/m), and both traveling in opposite directions results in w=sqrt(3k/m).

So I know that 3=2pi/w, but I don't know where that gets me.

I know that the answer to this question is t=sqrt(6) and t=3sqrt(2), but I can't imagine how these numbers and formulas can go together to make them.

 

[lanedance]

I'd start by setting up a matrix to describe the acceleration of each mass in terms of the position of each mass