# Math Help - Differential Equation Spring System!!!

1. ## Differential Equation Spring System!!!

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,