(10%) Problem 5: Near the top of the Citigroup Center building in New York City,
ID: 1793626 • Letter: #
Question
(10%) Problem 5: Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.2 x 105 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 x 105 kg t = 2.4s d = 2.6 m DA 50% Part (a) What effective force constant should the springs have to make them oscillate with a period of 2.4 s in N/m? Grade Summary k= | Deductions 0% Potential 100% sin() cos() tan() (D 7 8 9 HOME Submissions cotan() asin() acos() A 4 5 6 Attempts remaining: 5 atan() (5% per attempt) acotan() * 1 2 3 sinh) detailed view cosh() tanh) | cotanh) 0 END O Degrees O Radians VO BACKSPACE CLEAR Hint Feedback I give up! Submit Hints: 5% deduction per hint. Hints remaining: 2 Feedback: 5% deduction per feedback. E A 50% Part (b) What energy is stored in the springs for a 2.6 m displacement from equilibrium in J?Explanation / Answer
a)
mass m=4.2*10^5 kg
time period, T=2.4 sec,
force constant is k
time period T=2pi*sqrt(m/k)
2.4=2pi*sqrt(4.2*10^5/K)
force constant, K=2.88*10^6 N/m
b)
displacement x=2.6 m
enegry stored, U=1/2*k*x^2
U=1/2*(2.88*10^6)*2.6^2
U=9.7*10^6 J
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