Damped and Forced Harmonic Motion (AQA A-Level Further Maths): Flashcards

SHM with resistive force proportional to velocity

Oscillation about a moving equilibrium position

$\frac{d^2x}{dt^2} + k\frac{dx}{dt} + \omega^2 x = 0$

Resistance strength (larger $k$ = stronger resistance)

Discriminant $\Delta = k^2 - 4\omega^2$ of auxiliary eq.

$k^2 - 4\omega^2 > 0$ (positive)

$k^2 - 4\omega^2 < 0$ (negative)

Fastest approach to equilibrium without oscillating

CF + PI (Complementary Function + Particular Integral)

Opposes motion (opposite to velocity)