Since excitation is a simple harmonic i.e.

, hence

, where
{W} is a vector contains complex quantity i.e., magnitude and phase information of various displacement components.
Hence EOM can be written as

which can be solved as

where
is the rotor spin speed. It should be noted that matrices [M] and [K] contain real quantities, whereas force vector {F} and corresponding displacement vector {W} will contain complex terms.