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 https://instruct.math.lsa.umich.edu/...f6f80504a1.png and https://instruct.math.lsa.umich.edu/...6cee5510c1.png of the two masses are given by the system

Let https://instruct.math.lsa.umich.edu/...fc4a7ef6b1.png and https://instruct.math.lsa.umich.edu/...b7f133f941.png. If the forcing imparts a force https://instruct.math.lsa.umich.edu/...6243a8d041.png on the first mass and a force https://instruct.math.lsa.umich.edu/...62e09d3091.png on the second and the masses start from rest ( https://instruct.math.lsa.umich.edu/...df557324a1.png ) and at their equilibrium positions ( https://instruct.math.lsa.umich.edu/...e0baed2a91.png ), find the resulting motion of the system. https://instruct.math.lsa.umich.edu/...0b7a484251.png

https://instruct.math.lsa.umich.edu/...4023b3ad91.png

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 = $\displaystyle \begin{pmatrix}

{1}\\

{1}

\end{pmatrix}$

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

{-1}\\

{1}

\end{pmatrix}$

So,

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

Many thanks...