Question

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 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...

Answer 1

I think the question should be the below:

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

Answer is the below:

Acceleration .. a = (-) ω² x
(ω = equivalent ang. vel. = 2π.f) (x = displacement from equilibrium position)

x (max) = a(max) /ω²

x = (0.015 x 9.8m/s²) / (2π.f)² .. .. (0.147) / (2π*0.22)² .. .. ►x(max) = 0.077m .. (7.70cm)