Near the top of the Citigroup Bank building in New York City, there is a 4.00 10

Question

Near the top of the Citigroup Bank building in New York City, there is a 4.00 105 kg mass on springs having 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 mass, which oscillates instead of the building. (a) What effective force constant should the springs have to make the mass oscillate with a period of 5.00 s? N/m (b) What energy is stored in the springs for a 1.00 m displacement from equilibrium? J

Explanation / Answer

a)

mass m=4*10^5 kg

time period, T=5 sec,

force constant is k

time period T=2pi*sqrt(m/k)

5=2pi*sqrt(4*10^5/K)

==> K=631654.7 N/m

force constant, K=6.32*10^5 N/m

b)

displacement x=1m

enegry stored, U=1/2*k*x^2

U=1/2*(6.32*10^5)*1^2

U=3.16*10^5 J

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