Second order circuit

A second-order circuit is any electrical circuit that contains two energy storage elements (typically inductors and/or capacitors)

Step Response (with source)

With a step input VsV_sVs​, the response depends on damping:1. Overdamped (ζ>1)(\zeta > 1)(ζ>1)

Two real distinct roots

Slow, non-oscillatory response

2. Critically damped (ζ=1)

Repeated real root

Fastest non-oscillatory response

3. Underdamped (ζ<1)

Complex conjugate roots

Oscillatory (sinusoidal + exponential decay)