RLC circuit in free oscillation

Example 4 — RLC circuit in free oscillation

Resistance $R$, inductor $L$, capacitor $C$ in series: $L\ddot Q + R\dot Q + \frac{Q}{C} = 0.$ It is formally identical to the damped oscillator (mass-spring with friction) with the correspondences $m\leftrightarrow L$, $\gamma\leftrightarrow R/(2L)$, $\omega_0^2 \leftrightarrow 1/(LC)$.

The natural frequency is $\omega_0 = 1/\sqrt{LC}$. The three regimes are the same as for the mechanical oscillator: underdamped (the LC radio that “rings”), critically damped, overdamped.

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Topics: Differential equations
Concepts: Second-order linear ODE · Harmonic oscillator · Damping
Methods: Harmonic oscillator ODE
Skills: Modelling · Solving equations