Cable tension, deck mass and wind speed against resonance.
-Natural frequency f_n (Hz)
-Shedding frequency f_s (Hz)
-Resonant wind speed (m/s)
-Steady amplitude now (cm)
-Recent peak amplitude (cm)
-State
The science
A deck hung from taut cables behaves like a vibrating string: the restoring force is the cable tension, so mode n has frequency f_n = n / (2 L) sqrt(T / m). Heavier decks and longer spans lower it; more tension raises it.
Wind passing a bluff deck of depth D sheds vortices alternately above and below at f_s = St U / D (Strouhal number St ~ 0.2). Each vortex gives an alternating lift force 0.5 rho U^2 D C_L per metre, acting over a correlation length L_c. The deck mode follows the driven damped oscillator q'' + 2 z w q' + w^2 q = (Q / M) sin(2 pi f_s t) with modal mass M = m L / 2.
At resonance the amplitude is limited only by damping: q = Q / (2 z M w^2), so doubling the damping ratio halves the sway. The animation integrates this equation with fourth-order Runge-Kutta.
Honest simplifications: one mode at a time, a linear taut-string stiffness (no deck bending stiffness, no cable sag), a constant Strouhal number and no lock-in feedback. The 1940 Tacoma Narrows collapse was an aeroelastic flutter (self-excited), which this forced-vibration model does not capture.