# Homework Help: Two masses coupled with a spring

1. Dec 11, 2011

### Silken

Hi

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

Given is a system containing to masses m1 and m2 which are connected by a spring with spring constant k.Oscillation and translation is restricted to one dimension only.

2. Relevant equations

euqation of motion

3. The attempt at a solution

So, I can find out the equation of motion, which I done

$$m_{1} \ddot x_{1}=-k(x_{1}-x_{2})$$
$$m_{2} \ddot x_{2}=k(x_{1}-x_{2})$$

Now we solved it to find the equation of motion with a method, I don't understand. First of all: I got the solution, but I don't understand why we did this, would be awesome if someone could explain it to me.
First of all we wrote the 2 equations with the help of a matrix. Afterwards we were looking for the Eigenvalues (which are the frequency/frequencies <- I hope that's right). But after this step I don't understand what happens. We multiply the matrix with a vector, find the norm and finally get to the solution. I understand the final solution but not the 'way' of how I get there. The solution looks like

$$\vec x_{1}(t)=\vec v_{1}*(At+B)$$
$$\vec x_{2}(t)=\vec v_{2}*(Ccos( \omega t)+Dsin(\omega t))$$

which gives us the translation and the oscillation. I hope my text isn't too confusing as I'm just not sure about what 'happens' here to get to the solution. At our university, or rather at my study course, we don't get taught matrix calculus so I have trouble understanding this problem.