A forced undamped simple harmonic oscillator has the equation dy(t)/dt^2 + my(t) + ky(t) = f(t), where f(t) is a periodic function with period 4, and for -2 < t < 0 and 0 < t < 2, f(t) = 0.
(a) Find the complex exponential Fourier series for f(t).
(b) Assuming that y(t) is also a periodic function with period 4, find the complex exponential Fourier series for y(t).
(c) For what values of k/m will this method of finding y(t) fail?