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 3.00 s? n/m
(b) what energy is stored in the springs for a 2.00 m displacement from equilibrium?

(a) k = 1.76× 10⁶ N/m

(b) E = 3.52 × 10⁶ J

Explanation:

(a)

The period (T) of a spring = 2π√(m/k)

where m =  mass of the spring in kg, k = spring constant.

T = 2π√(m/k) equation 1

making k the subject of the equation,

k = 4π²(m)/T² equation 2

Where m = 4.00 × 10⁵ kg, T = 3.00 s, π = 3.143

Substituting these values into equation 2

k = 4(3.143)²(4.0×10⁵)/3²

k = (1.58 × 10⁷)/9

k = 1.76× 10⁶ N/m

(b)

The energy stored(E) in a  spring = 1/2ke²

Where k = spring constant, e = extension.

E = 1/2ke²

k = 1.76× 10⁶ N/m, e= 2.00 m

∴E = 1/2(1.76× 10⁶)(2)²

E = 2 × 1.76 × 10⁶

E = 3.52 × 10⁶ J

answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.