Engineering Handbook/Oscillation

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