# Coupled Harmonic Oscillator

1. Jun 11, 2008

### lylos

1. The problem statement, all variables and given/known data
Two masses are connected via a spring. Write the equations of motion, solve them (x(t)), and find the normal mode frequencies.

2. Relevant equations
F=ma
F=-kx

3. The attempt at a solution
I set up two equations:
$$F_{1}=ma_{1} , F_{2}=ma_{2}$$
$$-k(x_{2}-x_{1})=m\ddot{x_{1}} , k(x_{2}-x_{1})=m\ddot{x_{2}}$$

Then I solved the 2nd force equation for $$x_{1}$$ and plugged it into the first force equation resulting in:
$$-\ddot{x_{2}}=\ddot{x_{1}}$$

I really don't know what to do now... Any help would be greatly appreciated!