I have an equation of motion differential equation:
$$M\;x''(t) + C\;x'(t) + K\;x(t) = 0$$
I know $M,C,$ and $K$ (constant $4\times 4$ matrices) and also the eigenvalue-eigenvector pairs. What I do not know is how to get the general solution from this. I am using matlab.
The eigenvalue-eigenvector pairs solve the equation $\left(\lambda^2M + \lambda C + K\right)x = 0$