# Homework Help: Coupled oscillation

1. Sep 14, 2009

### Eric_meyers

1. The problem statement, all variables and given/known data
"A particle of mass m is attached to a rigid support by means of a spring of spring constant k. At equilibrium, the spring hangs vertically downward. An identical oscillator is added to this system, the spring of the former being attached to the mass of the latter. Calculate the normal frequencies for one-dimensional vertical oscillations, and describe the associated normal modes."

3. The attempt at a solution

So I drew the picture as a spring from a ceiling with a mass at the end of it coupled to another spring with a mass hanging down from that second spring.

I define x1 to be the displacement of the first block (nearest to ceiling) in the downward direction

I define x2 to be the displacement of the second block (farthest down) in the downward direction.

m x1'' = -kx1 - k(x1 + x2) + mg

m x2'' = -k(x2-x1) + mg

x1'' = -2w^2x1 - w x2 + g

x2'' = -w (x2 - x1) + g

Solving these equations by setting them up as a matrix...

( -2w^2, -w ) (x1) = (g)
( w , -w ) (x2) = (g)

I don't think I set it up right because I can't really solve this...