The New England Merchants Bank Building in Boston is 152m high. On windy days it sways with a frequency of 0.19Hz, and the acceleration of the top of the building can reach 2.3% of the free-fall acceleration, enough to cause discomfort for occupants.

What is the total distance, side to side, that the top of the building moves during such an oscillation?

Question

Konnor Simpson

Physics

19 February, 01:34

The New England Merchants Bank Building in Boston is 152m high. On windy days it sways with a frequency of 0.19Hz, and the acceleration of the top of the building can reach 2.3% of the free-fall acceleration, enough to cause discomfort for occupants.

What is the total distance, side to side, that the top of the building moves during such an oscillation?

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Answers (1)

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Sheppard · Answer 1

0.316 m.

Explanation:

Frequency, f = 0.19 Hz

Using curcular motion equation,

ω = 2π*f

= 1.19 rad/s

Maximum acceleration, a (max) = 2.3 % * 9.8m/s^2

= 0.023 * 9.8

= 0.225 m/s^2

In simple harmomic motion,

a (max) = A*ω^2

Where,

A = amplitude

= 0.225/1.19^2

= 0.158 m

2A = 0.316 m.