The New England Merchants Bank Building in Boston is 152 mm high. On windy days it...

The New England Merchants Bank Building in Boston is 152 mm high. On windy days it sways with a frequency of 0.19 HzHz , and the acceleration of the top of the building can reach 1.5 %% 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?

Expert Solution

Height of The New England Merchants Bank Building, h = 152 m

The frequency of oscillation of the building due to wind, f = 0.19 Hz

Acceleration of the top of the building, a = 1.5 % of free fall acceleration = 1.5 g/100

a = 1.5 x 9.8 /100 = 0.147 m/s2

angular frequency of vibration, ω = 2πf = 2 x 3.14 x 0.19 = 1.19 rad/s

maximum of acceleration due to vibration, a = Aω2

amplitude of vibration, A = a/ ω2 = 0.147/1.19 x 1.19 = 0.104m

the total side to side distance the building moves through during an oscillation,

x = 2A = 2 x 0.104 = 0.208 m

the total distance, side to side, that the top of the building moves during such an oscillation, x = 0.208 m

genius_generous answered 1 year ago

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