Thread: Differential Equation Spring System!!!

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 =

for lambda = -25 v2 =

So,

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


Many thanks...