Near the top of the Citigroup center building in New York City there is an objec

Question

Near the top of the Citigroup center building in New York City there is an object with mass of 3.6 times 10^5 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. Randomized Variables m = 3.6 times 10^3 kg t = 26 s d = 1.8m What effective force constant should the springs have to make them oscillate with a period of 2.6 sin N/m? What energy is stored in the springs for a 1.8 m displacement from equilibrium in

Explanation / Answer

(a) From T = 2(m / k) we get
k = 4²m / T² = 4² * 3.6e5kg / (2.60s)² = 2.102e6 kg/s² = 2.102e6 N/m

(b) U = ½kx² = ½ * 2.102e6N/m * (1.80m)² = 3.405e6 J

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