(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A system is connected as follows, going vertically downwards: (ceiling)-(spring with constant k)-(mass 1)- spring with constant k)-(mass 2)

Let x be the displacement from the equilibrium position of mass 1, and let y be the displacement from the equilibrium position of mass 2. Takedownwardsdisplacement as positive.

I'm trying to show that the angular frequencies of the normal modes are ω^2=(3±5)k/2m, but I'm stuck.

m(d^2x/dt^2)=mg-kx

m(d^2y/dt^2)=mg-k(y-x)

When I try to put this into matrix form, I can't get rid of the mg terms.

2. Relevant equations

3. The attempt at a solution

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# Equation of motion of coupled springs

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