Fundamental Physics/Formulas/Oscillation

Oscillation

A movement of matter about an equilibrium point over and over until equilibrium is reached over a time period . It is a periodic motion

Spring's Oscillation	Symbol	Horizontal	Vertical

Spring's Oscillation equation	$f^{''}(t)$	$m{\frac {d}{dt}}x(t)=-kx(t)$	$m{\frac {d}{dt}}y(t)=-ky(t)$
Spring's wave function	$f(t)$	$x(t)=ASin\omega t$ $\omega ={\sqrt {\frac {k}{m}}}$	$y(t)=ASin\omega t$ $\omega ={\sqrt {\frac {k}{m}}}$

Spring's Oscillation

Electric's Oscillation	RLC series at equilibrium	RLC series at resonance	LC series at equilibrium	LC series at resonance

Wave equation	${\frac {d^{2}}{dt^{2}}}i(t)=-2\alpha {\frac {d}{dt}}i(t)-\beta i(t)$	$Z_{L}=-Z_{C}.Z_{t}=R$	${\frac {d^{2}}{dt^{2}}}i(t)=-{\frac {1}{T}}$	$Z_{L}=-Z_{C}$
Wave function	$i(t)=A(\alpha )Sin\omega t$	$i(\omega =0)=0$ $i(\omega =\omega _{o})={\frac {v}{R}}$ $i(\omega =0))=0$	$i(t)=ASin\omega t$	$V_{L}=-V_{C}$
	$A(\alpha )=Ae^{-\alpha t}$
	$\omega ={\sqrt {\beta -\alpha }}$	${\sqrt {\frac {1}{T}}}$	${\sqrt {\frac {1}{T}}}$	${\sqrt {\frac {1}{T}}}$
	$\beta ={\frac {1}{T}}={\frac {1}{LC}}$
	$T=LC$	$LC$	$LC$	$LC$
	$\alpha =\beta \gamma ={\frac {R}{2L}}$
	$\gamma =RC$

Electromagnetic's Oscillation	Formula

Wave equation	$\nabla ^{2}E(t)=-\omega E(t)$ $\nabla ^{2}B(t)=-\omega B(t)$
Wave function	$E(t)=ASin\omega t$ $B(t)=ASin\omega t$ $\omega ={\sqrt {\frac {1}{T}}}=C=\lambda f$ $T=\mu \epsilon$

This article is issued from Wikiversity. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.