Damped and Driven Harmonic Oscillator - Fourier Series Solution

Damped and Driven Harmonic Oscillator - Fourier Series
Solution

Consider a driven damped mass on a spring system. You can vary the
driving frequency relative to the natural frequency, you can also vary
the damping relative to the natural freqency. The driving force will
be given as a step function, with the portion of the period that the
force is active being variable (DT/T).
Consider the image below:

The step-function driving force can be approximated as a Fourier
sine series, which will lead to a sine series as a response function:

Vary the driving freqency, the damping effect, and the number of
terms of the sine series to investigate the various effects on the
response function.