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Math Help - Differential Equation Spring System!!!

  1. #1
    Junior Member
    Joined
    Mar 2009
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    32

    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 = \begin{pmatrix}<br />
{1}\\ <br />
{1}<br />
\end{pmatrix}

    for lambda = -25 v2 = \begin{pmatrix}<br />
{-1}\\ <br />
{1}<br />
\end{pmatrix}

    So,

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


    Many thanks...
    Last edited by althaemenes; June 9th 2009 at 01:32 PM. Reason: miscalculation
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