Simple Harmonic Motion (Edexcel A-Level Further Mathematics): Flashcards

$m \frac{d^2x}{dt^2} + c \frac{dx}{dt} + kx = 0$

$c^2 < 4mk$

Oscillates with exponentially decaying amplitude

$c^2 = 4mk$

Returns to equilibrium without oscillating (fastest)

$c^2 > 4mk$

$x(t) = x_c + x_p$

Complementary function

Particular integral

Complex