Question

Tall buildings are designed to sway in the wind. In a 100km/h wind, suppose the top of a 110-story building oscillates horizontally with an amplitude of 17 cm at its natural frequency, which corresponds to a period of 6.1 s .

Assuming SHM, find the maximum horizontal velocity experienced by an employee as she sits working at her desk located on the top floor.

Find the maximum acceleration experienced by an employee as she sits working at her desk located on the top floor.

Compare the maximum acceleration (as a percentage) with the acceleration due to gravity.

Answer 1

T = 2pi squareroot m/k 6.1 = 2pi times squareroot m/k m/k = 0.971 1/2 kA^2 = 1/2mv^2 V^2_max = k/m times A^2 = 1/0.971 times (0.17)^2 V_max = 0.17 m/sec a_ma = KA/m = 0.17/0.971 = 0.175m/s^2 a/g = 0.0178 = 1.78%