Forced oscillations with periodic forcing functions

We use Fourier series for 2L-periodic piece-wise continuous forcing functions f(t) to precisely understand when undamped oscillators
x' ' (t) + a x(t) = f(t)
exhibit resonance; and to understand when slightly damped forced oscillators
x' ' (t) + c x' (t) + a x(t) = f(t)
exhibit practical resonance.