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27 September, 11:32

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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  1. 27 September, 14:39
    0
    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.
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