# Normal modes of a two mass, two spring system?

1. Apr 9, 2013

### Spiral1183

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

I have a system of two masses m1 and m2 coupled by two springs with constants k1 and k2. If m1 and m2 are equal what would be the normal modes for this system?

2. Relevant equations

Equations of motion for the system:
\begin{align*}
m_1\ddot{x}_1 &= -k_1x_1+k_2(x_2-x_1) \\
m_2\ddot{x}_2 &= -k_2(x_2-x_1)
\end{align*}

3. The attempt at a solution

I am having some serious trouble understanding how to come come up with the normal modes and thus the normal frequencies for this problem. I understand in a three spring system and have read examples of the two spring system, but am still struggling with how they came to their solution. Am I supposed to grind these problems out into a 4th order ODE, and if so where do I go from there?

Last edited by a moderator: Apr 10, 2013
2. Apr 9, 2013

### voko

A normal mode is $x_1 = A \sin at, \ x_2 = B \sin at$. Substitute this and determine a, A, B.

3. Oct 1, 2017

### rahaverhma

Why same frequency ?