Given that I have a matrix of second order differential equations of this form:

Where `M`

, `x`

, `C`

, `K`

are matrix and vectors.

I can decomposed the solutions into different eigenvalues and eigenvectors, as dictacted by the theory of eigenvalue problem, and then solve the equations for each mode of eigenvectors, provided that I have the initial condition for the `x`

and the first derivative of `x`

.

My question is, if the initial conditions are unknown, is there anyway I can still tell the relative magnitude for different eigenvectors?