Results from every tool here are for reference only. These are teaching simulations of idealised systems — check against other sources before relying on them.
Dynamics & feedback

Control Systems

Two interactive simulations of how systems respond and how we steer them — the second-order system that underlies almost everything that moves, and the controller that tames it.

PID Control

Tune proportional, integral, and derivative gains and watch the closed-loop step response settle, overshoot, or oscillate — live.

u = Kₚe + Kᵢ∫e dt + Kₐ·de/dt
Open

Mass-Spring-Damper

The canonical second-order system with animated playback — set the damping and watch it ring, settle critically, or crawl back overdamped.

m·x″ + c·x′ + k·x = 0
Open