Ask Question
28 July, 16:46

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?

+4
Answers (1)
  1. 28 July, 16:47
    0
    (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
Know the Answer?
Not Sure About the Answer?
Find an answer to your 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 ...” in 📗 Physics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers