Chapter 16 HW #1 Begin Date: 1/5/2018 12:00:00 AM-Due Date: 1/31/2018 11:59:00 P

Question

Chapter 16 HW #1 Begin Date: 1/5/2018 12:00:00 AM-Due Date: 1/31/2018 11:59:00 PM End Date: 5/19/2018 12:00:00 AM (13%) Problem 4: Near the top of the Citigroup Center building in New York City, there is an object with mass of 3.2 × 10, 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 = 3.2 x 105 kg t= 1.4 s d= 1.2 m 50% Part (a) what effective force constant should the springs have to make them oscillate wit a period of 1.4 s in N/m? Grade Summary Potential 100% sin cosO asino atan) acotan) sinho cosh( ) | tanh( ) cotanh( ) ODegrees Radians tan0 acoso 78 9 Attempts remaining: I (0% per attempt) detailed view cotan) 456 I give up! Hints:% deduction per hint. Hints remaining: 2 Feedback: deduction per feedback. 50% Part (b) What energy is stored in the springs for a 1.2 m displacement from equilibrium i J?

Explanation / Answer

A.

Time period is given by:

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

k = 4*pi^2*m/T^2

Using given values:

k = 4*pi^2*3.2*10^5/(1.4^2)

k = 6.445*10^6 N/m

B.

Potential energy is given by:

PE = 0.5*k*x^2

Using above value of k

PE = 0.5*6.445*10^6*(1.2)^2

PE = 4.64*10^6 J

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