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 4.2 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 = 4.2 Times 10^5 kg t= 1.4 s d = 1.8 m What effective force constant should the springs have to make them oscillate with a period of 1.4 s in N/m? Numeric : A numeric value is expected and not an expression. What energy is stored in the springs for a 1.8 m displacement from equilibrium in J? Numeric : A numeric value is expected and not an expression.

Explanation / Answer

force constant k = w^2 m = ( 2 pi/ T)^2 m = ( 2pi/1.4)^2 * 4.2 * 10^5 kg = 84.51 * 10^5 N/m

energy stored in the spring is

E = 1/2 * k x^2 = 1/2 *  84.51 * 10^5 N/m ( 1.8)^2 = 136.9 * 10^5 J

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