Does this explain the Tacoma Narrows Bridge failure?

Not by itself. The 1940 collapse involved large-amplitude torsional motion coupled to aerodynamic forces (flutter / limit-cycle behavior), not a simple mass–spring–dashpot resonance at a pedestrian cadence. This simulator is still useful for the general lesson: avoid exciting a natural frequency with sustained energy input.

Bridge Resonance (1-D mode)

Damped modal oscillator with harmonic drive: sweep ω near √(k/m) — presets for cadence-like and low-ζ peaks.

Live graphs

About this model

One flexural mode of a bridge span is approximated as a damped harmonic oscillator. A sinusoidal force models narrow-band loading — a teaching stand-in for rhythmic pedestrian loading or simplified buffeting. The steady-state amplitude versus drive frequency shows a resonance peak near the modal frequency; damping ratio ζ controls peak width and height.

Who it's for: Intro vibrations and structural dynamics; reading f₀ and comparing to drive frequency.

Key terms

resonance
modal frequency
damping ratio
harmonic drive
steady-state amplitude

How it works

A single flexural mode of a span is modeled as a damped harmonic oscillator driven by a sinusoidal force — a stand-in for rhythmic loading (march cadence) or narrow-band wind buffeting. Sweep the drive frequency near the modal frequency f₀ to see resonance: large amplitude for small ζ. The Tacoma Narrows collapse involved aeroelastic flutter and torsion, which is not the same as this linear SDOF picture, but the cartoon explains why matching a natural frequency matters.

Key equations

mẍ + bẋ + kx = F₀ cos(ωt), ω₀² = k/m

A = (F₀/m) / √((ω₀² − ω²)² + (bω/m)²) — Lorentzian-like peak vs ω when ζ ≪ 1

Frequently asked questions

Does this explain the Tacoma Narrows Bridge failure?: Not by itself. The 1940 collapse involved large-amplitude torsional motion coupled to aerodynamic forces (flutter / limit-cycle behavior), not a simple mass–spring–dashpot resonance at a pedestrian cadence. This simulator is still useful for the general lesson: avoid exciting a natural frequency with sustained energy input.

Continue with similar topics in this category — or all 85 in Classical Mechanics.

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