If the generalized driving forces Qi are not sinusoidal, show that the forced vibrations o...

If the generalized driving forces Qi are not sinusoidal, show that the forced vibrations of the normal coordinates in the absence of damping are given by

where Gi(ω) is the Fourier transform of Qi defined by

If the dissipation function is simultaneously diagonalized along with T and V, show that the forced vibrations are given by

which has the typical resonance denominator form. These results are simple illustrations of the powerful technique of the operational calculus for handling transient vibrations.