Mr. IntegralFourier Series and Periodic Forcing — Cheat sheet
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Core rule
Compute harmonic coefficients, apply each frequency response, then superpose where convergence justifies it.
Watch for
A finite Fourier sum overshoots near a jump; adding terms narrows the affected region but does not eliminate the limiting Gibbs overshoot. For an undamped oscillator, a resonant harmonic needs separate treatment because no bounded steady periodic response exists.