Reverse transformation [u] = [\[CapitalPhi]N] [q]?

The two equations of motion were modally decoupled with the generalized eigenvalues [[CapitalPhi]N].
How can I perform the reverse transformation [u] = [[CapitalPhi]N] [q]?
What do I have to consider when plotting the results?

Beispiel für Frage von Bernhard Michels.nb (9.18 KB)