Part A What is the total distance, side to side, that the top of the building mo

Question

Part A

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

The New England Merchants Bank Building in Boston is 152 m high. On windy days it sways with a frequency of 0.22 Hz , and the acceleration of the top of the building can reach 2.5 % of the free-fall acceleration, enough to cause discomfort for occupants.

You may want to review ( pages 444 - 448) .

Part A

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

Explanation / Answer

The maximum acceleration is a = A*^2 = 0.025*9.81 = 0.24525 m/s^2

Radian frequency = 2pi*f = 2pi*0.22 Hz = 1.382 rad/s

so the amplitude of oscillation is A = 0.24525 / 1.382^2 = 0.12835 m

so the total side-to-side distance is 2A = 0.2567 m (= 25.67 cm)

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