# Equation of motion of coupled springs

1. Jan 29, 2012

### Lucy Yeats

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. Take downwards displacement 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

2. Jan 29, 2012

### vela

Staff Emeritus
Note the bolded phrases. The mg terms shouldn't be there in the first place.

By the way, I've moved this thread to the advanced physics forum since it looks like a problem from an upper-division classical mechanics course or math methods course.

3. Jan 29, 2012

### Lucy Yeats

So I don't need the mg terms because they only affect the equilibrium position?
So if I cross out those terms will the equations be right?

4. Jan 29, 2012

### vela

Staff Emeritus
Right. When x=0, mass 1 is at its equilibrium position, so the net force on it is equal to 0. The same holds for mass 2 and (y-x)=0.