(14%) Problem 3: Near the top of the Citigroup Center building in New York City,

Question

(14%) Problem 3: Near the top of the Citigroup Center building in New York City, there is n object with mass of, 10 kg on springs that have adjustable force constants. Its fiunction is to dampen wind-driven oscillations of the building by oscillat ing at the same frequency as the building is being driven he driving force is transferred to the object, which oscillates instead of the entre building. Randomized Variables n-3.4 × 105 kg t- 1.2s d=2.2 m 50% Part (a) what effective force constart should the springs have to make then, oscillate with a period of .2 sin Nin? 50% Part (b) what energy is stored m the springs for a 2.2 m displacement from equilibrium in J?

Explanation / Answer

(a)

T = 1.2 s

Time period for a SHM is given by ,

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

1.2 = 2*3.14 * sqrt((3.4*10^5)/k)

1.2 = 6.28 * sqrt((3.4*10^5)/k)

1.2/6.28 = sqrt((3.4*10^5)/k)

(0.191)^2 = (3.4*10^5)/k

k = (3.4*10^5)/(0.191)^2

Solving for k

k = 9.32*10^6 N/m

Effective force constant should the spring have, k = 9.32*10^6 N/m

(b)

Energy Stored in Spring, = 1/2 * kx^2

E = 1/2 * 9.32*10^6 * 2.2^2 J

E = 2.255*10^7 J

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