The jumper falls freely under gravity until they have descended the cord's unstretched natural length L₀. Past that point the cord stretches, and — because a real elastic cord can only pull, never push — a Hookean restoring force F = −k(x − L₀) switches on only while the cord is taut; it is exactly zero the instant the cord goes slack again. Two damping terms bleed energy from the system: quadratic air drag (∝ v|v|) acting the whole flight, and an extra linear cord-internal damping c·v that only applies while the cord is stretched, modelling the rope's own hysteresis. The simulator integrates Newton's second law m·a = mg − Fspring − Fdrag − Fdamp every frame with a fixed-step semi-implicit Euler scheme — nothing about the bounce trajectory is scripted or eased.
x = distance fallen from platform
stretch = max(0, x − L0)
F_spring = k · stretch (0 when slack)
F_damp = c · v · [stretch > 0]
F_drag = 0.5·ρ·Cd·A · v·|v|
a = g − (F_spring + F_damp + F_drag) / m
v += a·dt ; x += v·dt
- Cord stiffness k — a stiffer cord decelerates the fall harder and sooner, but also snaps back with more force, producing sharper, faster oscillations.
- Natural length L₀ — how far the jumper free-falls before the cord starts pulling; too long relative to the platform height risks hitting the ground before the cord ever engages.
- Damping c — energy the cord itself dissipates each stretch cycle; higher damping shrinks each successive bounce faster, settling to a stable hang point sooner.
- Lowest point / outcome — the true minimum of the integrated trajectory, not a preset number — raise k or shorten L₀ to turn a "crash" into a "safe" clearance.
Real-world relevance: this is the same damped-harmonic-oscillator model (mass–spring–damper) used to size real bungee cords, vehicle suspension, and building seismic dampers — energy stored elastically on the way down is returned on the way up, minus whatever the damping terms remove each cycle.