Tacoma Narrows Bridge (1940)
Opened July 1. Collapsed Nov 7 — just 4 months later. Wind at 42 mph drove torsional oscillations at the bridge's natural frequency (~0.2 Hz). Amplitude grew until failure.
Equation of Motion:
ẍ + 2ζω₀ẋ + ω₀²x = F·cos(ωt)
At resonance (ω=ω₀): amplitude = F/(2ζω₀²)
Q = 1/(2ζ) — quality factor
Mode Shapes:
Real bridges have many modes. The Tacoma bridge had a torsional mode at 0.2 Hz that matched aerodynamic forcing.
Opened July 1. Collapsed Nov 7 — just 4 months later. Wind at 42 mph drove torsional oscillations at the bridge's natural frequency (~0.2 Hz). Amplitude grew until failure.
Equation of Motion:
ẍ + 2ζω₀ẋ + ω₀²x = F·cos(ωt)
At resonance (ω=ω₀): amplitude = F/(2ζω₀²)
Q = 1/(2ζ) — quality factor
Mode Shapes:
Real bridges have many modes. The Tacoma bridge had a torsional mode at 0.2 Hz that matched aerodynamic forcing.