Tall buildings are designed to sway in the wind. In a 100 km/hr wind ,for exampl

Question

Tall buildings are designed to sway in the wind. In a 100 km/hr wind ,for example, the top of the 110 story Sears Tower oscillates horizontally with an amplitude of 15 cm.The building oscillates at its natural frequency, which has a period of 7.0 s. Assuming Simple Harmonic Motion, find the maximum horizontal velocity and acceleration by a Sears employee as she sits working at her desk located on the top floor. Compare the maximum acceleration (as a percent) with the acceleration due to gravity.

Explanation / Answer

w = 2pi/T = 2pi/7 = 0.8976 rad/s let the equation for the horizontal displacement is y = 0.15sin(0.8976t) 1) --> v = 0.15*0.8976cos(0.8976t) and v max = 0.15*0.8976 = 0.1346 m/s ----------- 2) a) = -0.15*0.8976^2*sin(0.8976t) a max = 0.15*0.8976^2 = 0.1208 m/s^2 ------- 3) 0.1208 = 0.1208*100/9.81 % = 1.23%

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