Transients & Timing

Underdamped, Critically Damped & Overdamped Second-Order RLC Lab

Compare all three classic second-order differential equation step responses by tuning series resistance R across 2√(L/C).

Speed
Square-wave excitation (40 Hz) drives an underdamped L = 25 mH and C = 10 µF resonant tank (f0 ≈ 318 Hz), producing classic damped ringing on every edge!
● CH1: CH1
● CH2: CH2

Engineering Theory & Mathematical Model

R_critical = 2 × √(L / C) = 2 × √(0.025 / 0.00001) = 100 Ω

Every second-order electrical or mechanical system shares the characteristic polynomial s² + 2ζω₀s + ω₀² = 0. With L = 25 mH and C = 10 µF, critical resistance is exactly 100 Ω: below 100 Ω roots are complex conjugates (ringing); at 100 Ω fastest non-oscillatory settling occurs; above 100 Ω sluggish overdamped response dominates.

Interactive Lab Procedure

  1. Test R1 = 8 Ω (zeta = 0.08): strong underdamped ringing.
  2. Set R1 = 100 Ω (zeta = 1.00): crisp, fastest settling with zero overshoot!
  3. Set R1 = 350 Ω (zeta = 3.50): slow overdamped exponential creep.

Technical FAQ

What is the core governing formula for Underdamped, Critically Damped & Overdamped Second-Order RLC Lab?

R_critical = 2 × √(L / C) = 2 × √(0.025 / 0.00001) = 100 Ω — Every second-order electrical or mechanical system shares the characteristic polynomial s² + 2ζω₀s + ω₀² = 0. With L = 25 mH and C = 10 µF, critical resistance is exactly 100 Ω: below 100 Ω roots are complex conjugates (ringing); at 100 Ω fastest non-oscillatory settling occurs; above 100 Ω sluggish overdamped response dominates.

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.

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