Differential Equation Spring System!!!

althaemenes · #1 $Old$ June 9th, 2009, 06:00 AM

Hi, Please help me out with the following problem:

Problem:

Consider the double mass spring system shown in the figure below.

The positions

and

of the two masses are given by the system

Let

and

. If the forcing imparts a force

on the first mass and a force

on the second and the masses start from rest (

) and at their equilibrium positions (

), find the resulting motion of the system.

I have to find x_1 and x_2 solution...

Attempt:

First I found the eigen values which are 16 and 24. Then found the respective eigenvectors:

for lambda = -9 v1 = $\begin{pmatrix} {1}\\ {1} \end{pmatrix}$

for lambda = -25 v2 = $\begin{pmatrix} {-1}\\ {1} \end{pmatrix}$

So,

After that I am stuck... Please help...

Many thanks...