Taipei 101 (a 101-stor y building in Taiwan) is sited in an area that is prone t

Question

Taipei 101 (a 101-story building in Taiwan) is sited in an area that is prone to earthquakes and typhoons, both of which can lead to dangerous oscillations of the building.  To reduce the maximum amplitude, the building has a tuned mass damper, a 660,000 kg mass suspended from 42 in long cables that oscillates at the same natural frequency as the building.  When the building sways, the pendulum swings, reaching an amplitude of oscillation of the building.  

a.  What is the period of oscillation of the building?

b.  During strong winds, how fast is the pendulum moving when it passes through the equilibrium position?  

Explanation / Answer

since the natural frequency of the building is the same as the mass suspended from the cables, we can use a simple harmonic motion model to solve this.

first find the period of the mass suspended from the cords (damping doesn't have any part in this problem).

(a) T=2pi*sqrt(L/g)

T=2pi*sqrt(42m/9.8m/s^2)

T=13.007s --->13s

(b) since we are dealing with SHM we can use the Vmax equation to find the maximum velocity of the mass as it passes through the equilibruim point.

Vmax=2pi*f*A

since f=1/T we can plug in the period found in part (a) and Amplitude (A) is given in the information above A=75cm ---> 0.75m

Vmax=2pi*(1/13.007s)*(.75m)

Vmax=0.362m/s

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