The New England Merchants Bank Building in Boston is 152 mm high. On windy days it sways with a frequency of 0.20 HzHz , and the acceleratio

Question

The New England Merchants Bank Building in Boston is 152 mm high. On windy days it sways with a frequency of 0.20 HzHz , and the acceleration of the top of the building can reach 2.5 %% 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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Gia Bảo 3 years 2021-09-04T15:52:16+00:00 1 Answers 20 views 0

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  1. Neala
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    2021-09-04T15:54:06+00:00
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    Answer:

    The total distance, side to side, that the top of the building moves during such an oscillation = 31 cm

    Explanation:

    Let the total side to side motion be 2A. Where A is maximum acceleration.

    Now, we know know that equation for maximum acceleration is;

    A = α(max) / [(2πf)^(2)]

    So 2A = 2[α(max) / [(2πf)^(2)] ]

    α(max) = (0.025 x 9.81) while frequency(f) from the question is 0.2Hz.

    Therefore 2A = 2 [(0.025 x 9.81) / [((2π(0.2)) ^(2)] ] = 2( 0.245 / 1.58) = 0.31m or 31cm

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