How Can We Determine the Motion of a Compound Harmonic Mechanical System?

[qspeechc]

Homework Statement

http://img209.imageshack.us/my.php?image=springzu4.png
Determine the motion of this mechanical system satisfying the initial conditions :-
y1(0) = 1
y2(0) = 2
y1'(0) = -2*sqrt(6)
y2'(0) = sqrt(6)

Hint : there are 4 different methods you can use to solve this problem. They all give the same exact result.

I need to know what y1(t) and y2(t) are, please

Homework Equations

I know the shm equations- are they valid here?

The Attempt at a Solution

total k = 1/(1/k1+1/k2)

total m = m1 + m2

 

[blochwave]

I believe this problem is going to be a set of coupled differential equations

you can use linear algebra techniques to decouple them, or just brute force if you're unfamiliar with that.

I think it will proceed similarly to this https://www.physicsforums.com/archive/index.php/t-203860.html except his setup is different