Near the top of the Citigroup Center building in NYC, there is an object with ma

Question

Near the top of the Citigroup Center building in NYC, there is an object with mass of 3.2 x 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.

t= 1.2s

d=1.6m

- what effective force constant should the springs have to make them oscillate with a period of 1.2s in N/m?

- what energy is stored in the springs for a 1.6m displalcement from equilibrium in J?

Explanation / Answer

(1) T = 2 pi . sqrt (m/k)

1.2 = 2 x pi x sqrt(3.2 x 10^5/k)

0.190985932 = sqrt(3.2 x 10^5/k) = 565.685425 x sqrt (1/k)

sqrt(1/k) = 0.000337618619

squaring both sides

1/k = 1.13986332 x 10^-7

k = 8772981.66 N/m

(2) Energy = 1/2 kx^2

E = .5 x 8772981.66 x (1.6)^2

E = 11229416.5 J

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