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Characteristics Equations, Overdamped-, Underdamped-, …

Kevin D. Donohue, University of Kentucky1 Characteristics Equations, overdamped -, underdamped -, and critically damped CircuitsKevin D. Donohue, University of Kentucky2In previous work, circuits were limited to one energy storage element, which resulted in first-order differential equations. Now, a second independent energy storage element will be added to the circuits to result in second order differential equations:xadtdxadtxdty2122)(++=Kevin D. Donohue, University of Kentucky3 Find the differential equation for the circuit below in terms of vc and also terms of iLShow:vs(t)RLC+vc(t)_iL(t)cccscccsvLCdt dvLRdtvdLCtvvdtdvRCdtvdLCtv1)( )(2222++= ++= ++= ++=tLLLstLLLsdiLCiLRdtdiLtvdiCRidtdiLtv )(1)( )(1)(Kevin D.

Critically Damped Circuits. Kevin D. Donohue, University of Kentucky 2 In previous work, circuits were limited to one energy storage element, which resulted in first-order differential equations. Now, a second independent energy storage element will be added to the circuits to

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