Engineering Handbook/Oscillation

Oscillation	Formula
-->	$-Fx=F$ $-kx=m\frac{d^{2}x}{d{t}^2}$ $\frac{d^{2}x}{d{t}^2}+\frac{k}{m}=0$ $s^2+\frac{k}{m}=0$ $s=\pm \sqrt{-\frac{k}{m}}t$ $s=\pm j\omega t$ $x=e^{(\pm j\omega t)}$ $x=e^{(j\omega t)}+e^{(-j\omega t)}$ $x=ASin\omega t$
	$-Fy=F$ $-ky=m\frac{d^{2}y}{d{t}^2}$ $\frac{d^{2}y}{d{t}^2}+\frac{k}{m}=0$ $s^2+\frac{k}{m}=0$ $s=\pm \sqrt{-\frac{k}{m}}t$ $s=\pm j\omega t$ $y=e^{(\pm j\omega t)}$ $y=e^{(j\omega t)}+e^{(-j\omega t)}$ $y=ASin\omega t$
	$\frac{{\mathrm{d}}^2\theta }{\mathrm{d}{t}^2}+\frac{g}{\ell }\theta =0$ $\theta (t)={\theta }_0\cos \left(\sqrt{\frac{g}{\ell }}t\right)|{\theta }_0|\ll 1$