Is it Possible to Find out The Relative Magnitude of Different Modes in MultiDOF Second Order Differential Equations Without Knowing the Detail Initial Condition

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?