Simple Harmonic Motion (AQA A-Level Further Maths): Flashcards

$\frac{d^2x}{dt^2} = -\omega^2 x$

Angular frequency

$v = \omega\sqrt{a^2 - x^2}$

$T = \frac{2\pi}{\omega}$

$v_{\text{max}} = \omega a$

At centre of motion ($x = 0$)

$x = a\sin(\omega t)$ or $x = a\cos(\omega t)$

Amplitude (max displacement from centre)

$m = \pm \omega i$

$x = A\cos(\omega t) + B\sin(\omega t)$