Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.8 x 105 kg on springs that have adjustable

Question

Near the top of the Citigroup Center building in New York City, there is an object with mass of 4.8 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 X 50%
Part (a) What effective force constant, in N/m, should the springs have to make them oscillate with a period of 1.2 s? k = 9.5 * 106 9500000 X Attempts Remain 50%
Part (b) What energy, in joules, is stored in the springs for a 1.6 m displacement from equilibrium?

in progress 0
Maris 4 years 2021-09-01T09:34:17+00:00 1 Answers 50 views 0

Answers ( )

  1. ThanhThu
    0
    2021-09-01T09:35:57+00:00
    Reply

    Answer:

    The force constant is  k =1.316 *10^{7} \ N/m

    The energy stored in the spring is  E = 1.68 *10^{7} \ J

    Explanation:

    From the question we are told that

       The mass of the object is  M = 4.8*10^{5} \ kg

        The period is T = 1.2 \ s

    The period of the spring oscillation is  mathematically represented as

             T =2 \pi \sqrt{ \frac{M}{k}}

    where  k is the force constant

       So making k the subject

           k = \frac{4 \pi ^2 M }{T^2}

    substituting values

           k = \frac{4 (3.142) ^2 (4.8 *10^{5}) }{(1.2)^2}

          k =1.316 *10^{7} \ N/m

    The energy stored in the spring is mathematically represented  as

           E = \frac{1}{2} k x^2

    Where x is the spring displacement which is given as

            x = 1.6 \ m

    substituting values

          E = \frac{1}{2} (1.316 *10^{7}) (1.6)^2

           E = 1.68 *10^{7} \ J

       

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )