Compound Harmonic Motion

1. The problem statement, all variables and given/known data

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

2. Relevant equations
I know the shm equations- are they valid here?

3. The attempt at a solution

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

total m = m1 + m2

Help!

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