Series RLC Circuit

What you'll learn

How electrical circuits map to the same ODE structures as mechanical systems
Underdamped oscillation in a different physical domain
The effect of resistance, inductance, and capacitance on transient response

A series RLC circuit driven by a step voltage source. The inductor and capacitor trade energy back and forth, producing oscillating current and voltage — the electrical analogue of the mass-spring-damper. The resistor dissipates energy, damping the oscillation over time.

L \frac{d i _{L}}{d t} C \frac{d V _{c}}{d t} = V_{0} - R i_{L} - V_{c} = i_{L}

Notice this is the same structure as the mass-spring-damper: inductance plays the role of mass, capacitance is the inverse of stiffness, and resistance is damping. Simulate to see the transient response.

Things to try

Increase R to 50 — the circuit becomes overdamped and the capacitor charges without ringing.
Set R = 0 for an ideal LC circuit — the oscillation never decays.
Try C = 1e-4 — smaller capacitance means faster oscillations (higher natural frequency).
Compare the electrical analogy: L ↔ mass, 1/C ↔ stiffness, R ↔ damping coefficient.

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