The millennium bridge in London had to be closed soon after its opening because

Question

The millennium bridge in London had to be closed soon after its opening because of an uncomfortably large swaying motion. The cause was resonance between a natural mode of lateral oscillations of the bridge (frequency fo 1 Hz) and a fluctuating, sideways force exerted by the average person as they walk (at frequency f 1 Hz). If the damping constant of the bridge was b = 1.1 × 104 kg s-1 and the magnitude of the sideways walking force of a typical person is 25 N, estimate the full side-to-side amplitude of the bridge sway that would occur when 300 people, walking in unison, were crossing it.

Explanation / Answer

We know Fo = 25N * No. of people = 25 * 300 = 7500 N

damping factor = b = 1.1 * 104

Driving frequency = v = 1

Amplitude = 7500/ (2*pi)*b*v

=> Amplitude = 7500/ (2*3.14)*1.1 * 104 *1 = 1085.69 * 10-4 m

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