A series LCR circuit has inductance

PHYSICS · Multi-part · Fermi University Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations · Simple, damped and driven oscillations

Mathematical Methods for Physics, Ch Second-order linear equations: damping, driving and resonance

Problem

A series LCR circuit has inductance Lc=2.0 HL_{\mathrm{c}} = 2.0\,\mathrm{H}, resistance R=20 ΩR = 20\,\Omega and capacitance C=0.020 FC = 0.020\,\mathrm{F}, with no source connected. The charge qq on the capacitor obeys Lcq¨+Rq˙+q/C=0L_{\mathrm{c}}\ddot{q} + R\dot{q} + q/C = 0. ((a)) Write down ω0\omega_0 and γ\gamma for this circuit. ((b)) Write the auxiliary equation and solve it for λ\lambda. ((c)) State which damping regime this is.

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