Same real mechanism as the 3D Tacoma Narrows scene, reduced to one number: the twist angle θ of the deck's midspan cross-section, governed by a damped, driven torsional oscillator —
I·θ'' + c(V)·θ' + k·θ = F(V)·sin(ω_shed·t)
Vortex shedding off the bluff girder drives the deck at a frequency set by the Strouhal relation, f_shed = St·V/D — it rises with wind speed V and falls as the deck depth D grows. When f_shed drifts close to the deck's own natural torsional frequency f₀ = ω₀/2π, the forced response amplifies, exactly as any resonant oscillator would.
The 1940 collapse was not only that: real bridges under strong crosswind experience a torsional flutter derivative — an aerodynamic moment that grows with the deck's own twisting velocity θ'. Below a critical wind speed it adds a small extra drag; above it, it acts as negative damping, feeding energy into the twist on every cycle instead of removing it. This sim reproduces that switch directly in the damping term:
c(V) = c₀ − c₁·max(0, V − V_crit)
Once c(V) turns negative, the amplitude no longer settles to a steady forced response — it grows cycle over cycle without any further increase in wind speed, the runaway self-excited flutter that tore the real deck apart. This is a simplified single-degree-of-freedom pedagogical model, not a full unsteady-aerodynamics flutter simulation, but it captures the qualitative story: resonance narrows the gap, and negative aerodynamic damping past a critical speed is what actually breaks it.
- Wind gust — injects a brief extra push, useful for probing stability near the critical speed.
- Collapse — once |θ| passes a structural limit, the deck is treated as failed and the run freezes for inspection.