🧪 Bungee Jump Simulator: Damped Cord Oscillation

A bungee jump is a textbook damped harmonic oscillator hiding inside an adrenaline sport. This simulator integrates the real second-order equation of motion: free fall under gravity, a piecewise Hookean restoring force that only exists while the elastic cord is stretched taut, quadratic air drag, and a cord-internal damping term. Nothing about the resulting bounce is scripted — tune cord stiffness, natural length, damping and jumper mass, and watch the height-vs-time and velocity-vs-time traces show the decaying oscillation settle to a stable hang point, or reveal a lowest point that dips below the ground for a "crash" outcome.