Given that I have a matrix of second order differential equations of this form:
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
My question is, if the initial conditions are unknown, is there anyway I can still tell the relative magnitude for different eigenvectors?