Near the top of the citigroup center building in New York City, there is an obje

Question

Near the top of the citigroup center building in New York City, there is an object with mass of 3.4x105 kg on springs that have adjustable force constants. Its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven -- the driving force is transferred to the object, which oscillates instead of the entire building.

(Part A) What effective force constant should the springs have to make them oscillate with a period of 1.6 s in N/m?

(Part B) What energy is stored in the springs for a 2.6 m displacement from equilibrium in J?

Explanation / Answer

(a)
T = 1.6 s
Time period for a SHM is given by ,
T = 2*pi * sqrt(m/k)
1.6 = 2*3.15 * sqrt((3.4*10^5)/k)
Solving for k
k = 5.27 * 10^6 N/m
Effective force constant should the spring have, k =  5.27 * 10^6 N/m

(b)
Energy Stored in Spring, = 1/2 * kx^2
E = 1/2 * 5.27 * 10^6 *2.6^2 J
E = 1.78 * 10^7 J

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