# Eigenvectors of coupled 2 different mass system

1. Sep 17, 2011

### physics-1

1. The problem statement, all variables and given/known data
Solve the coupled mass spring problem for two different masses. Similar to the Shankar example:
(d/dt)2x1=-2*w1*x1 + w1*x2
(d/dt)2x2=w2*x1 -2*w2*x2

where
w1= k/m1
w2 = k/m2

2. Relevant equations
Eigenvalue problem: UX=uX
Diagonalization: A=UDUt
Exponential Matrices: eA

3. The attempt at a solution
Starting off is simple enough. Taking the eigenvalue problem and solving for the eigenvalues.
L1 = -(w1+w2)+sqrt[ (w1+w2)2 - 3w1w2]
and L2 is the same as L1 but a minus in front of the sqrt

My problem lies when plugging back in the eigenvalues to solve for the eigenvectors. It seems straightforward but it is not. When plugging eigenvalues back into the matrix, trying to solve for eigenvector solution for both equations within the matrix is a tricky task.
Does anyone here know any required tricks that are needed to solve for the eigenvectors?

Many books stray away from this problem and resort to the system where the two masses are the same.
Any help is really appreciated.

2. Sep 18, 2011

### physics-1

Please disregard this posting. I have figured the solution.