Fundamental Physics/Formulas/Electric Oscillation

Electric 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	$x(t)=A(\alpha )Sin\omega t$	$i(\omega =0)=0$ $i(\omega =\omega _{o})={\frac {v}{R}}$ $i(\omega =0))=0$	$i(t)=ASin\omega t$	$V_{L}=-V_{C}$
	$A(\alpha )=Ae^{-\alpha t}$
	$\omega ={\sqrt {\beta -\alpha }}$	${\sqrt {\frac {1}{T}}}$	${\sqrt {\frac {1}{T}}}$	${\sqrt {\frac {1}{T}}}$
	$\beta ={\frac {1}{T}}$
	$T=LC$	$LC$	$LC$	$LC$
	$\alpha =\beta \gamma$
	$\gamma =RC$

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