Engineering

Second-Order Step Response

y = 1 − e^(−ζt)·(cos ω_d t + ζ/ω_d · sin ω_d t)

Raising the damping ratio ζ tames an underdamped system: the overshoot and ringing shrink as the step response settles ever more gently toward unity.

Computed & rendered in pure C# on the frozen OnlyCSharp 1.8 library — animation baked to GIF with the library's own Gif encoder (no GPU, no ffmpeg, no external packages).