(adsbygoogle = window.adsbygoogle || []).push({}); 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)^{2}x_{1}=-2*w_{1}*x_{1}+ w_{1}*x_{2}

(d/dt)^{2}x_{2}=w_{2}*x_{1}-2*w_{2}*x_{2}

where

w_{1}= k/m_{1}

w_{2}= k/m_{2}

2. Relevant equations

Eigenvalue problem: UX=uX

Diagonalization: A=UDU^{t}

Exponential Matrices: e^{A}

3. The attempt at a solution

Starting off is simple enough. Taking the eigenvalue problem and solving for the eigenvalues.

L1 = -(w_{1}+w_{2})+sqrt[ (w_{1}+w_{2})^{2}- 3w_{1}w_{2}]

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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Eigenvectors of coupled 2 different mass system

**Physics Forums | Science Articles, Homework Help, Discussion**