RLC Transient Circuit Response

Second-order differential equation solver modeling series RLC circuits across Underdamped, Critically Damped, and Overdamped states.

Instrument State:Live Analytical DSP Engine

2nd-Order Transient Analysis

Solves L(d²i/dt²) + R(di/dt) + i/C = 0 with characteristic roots and dynamic decay envelopes.

PRESETS:

underdamped

DAMPING RATIO (ζ)0.500ζ < 1 (Oscillates)

NATURAL FREQ (f₀)1.59 kHzω₀ = 10,000 rad/s

QUALITY FACTOR (Q)1.00α = 5,000 Np/s

PEAK OVERSHOOT (Mₚ)16.3%tₛ ≈ 0.80 ms

Series Resistor (R)100 Ω

Inductance (L)10 mH

Capacitance (C)1 µF

Damping Factor (ζ)ζ < 1 (Under), ζ = 1 (Critical), ζ > 1 (Over)

Resonant Frequencyω0 = 1 / √(L·C)

Quality FactorQ = (1/R) · √(L/C)

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