Engineering Theory & Mathematical Model
In a second-order series RLC circuit, energy sloshes back and forth between the capacitor electric field (½CV²) and the inductor magnetic field (½LI²) at the resonant frequency f₀ = 1/(2π√LC). When damping ratio ζ < 1 (R < 2√(L/C)), step edges excite underdamped sinusoidal ringing that decays exponentially as e^(−Rt/2L). Increasing R past critical damping (2√(L/C) = 100 Ω here) eliminates overshoot completely.
Interactive Lab Procedure
- Inspect the amber CH2 trace showing classic underdamped ringing on every rising and falling edge of the 40 Hz square wave.
- Click resistor R1 (8 Ω) and raise it slowly to 100 Ω to witness the exact transition from Underdamped to Critically Damped!
- Change the source waveform from Square to Sine and tune frequency to 318 Hz to observe resonant voltage magnification across C1.
Technical FAQ
What is the core governing formula for RLC Series Resonance & Underdamped Ringing Simulator?
f0 = 1 / (2π√(LC)), Q = (1/R)√(L/C), ζ = (R/2)√(C/L) — In a second-order series RLC circuit, energy sloshes back and forth between the capacitor electric field (½CV²) and the inductor magnetic field (½LI²) at the resonant frequency f₀ = 1/(2π√LC). When damping ratio ζ < 1 (R < 2√(L/C)), step edges excite underdamped sinusoidal ringing that decays exponentially as e^(−Rt/2L). Increasing R past critical damping (2√(L/C) = 100 Ω here) eliminates overshoot completely.
Can I modify component values and rewire this circuit live?
Yes! The schematic above runs a live MNA SPICE engine. Click any part to adjust parameters, add or delete wires and components, and click Share URL to save your custom topology.