What is the mass of the oscillating body of a spring pendulum if its maximum kinetic energy is 0.18 J

| February 26, 2021 | education

What is the mass of the oscillating body of a spring pendulum if its maximum kinetic energy is 0.18 J, the oscillation period is 2 s, and the amplitude is 6 cm? What is the potential energy of the body at a displacement equal to the amplitude?

Problem data: Ek (maximum kinetic energy of a given oscillating body) = 0.18 J; T (period) = 2 s; A – vibration amplitude (T = 6 cm = 0.06 m).

1) Stiffness of the spring pendulum: Епол = Ek = k * A ^ 2/2, from where we express: k = 2 * Ek / A ^ 2 = 2 * 0.18 / 0.06 ^ 2 = 100 N / m.

2) Mass of the vibrating body: T = 2 * Π * √ (m / k) and m = k * T ^ 2 / (4 * Π ^ 2) = 100 * 2 ^ 2 / (4 * 3.14 ^ 2) = 10.14 kg.

3) With a displacement equal to the amplitude, the entire kinetic energy of the spring pendulum will transform into potential energy and Ep = Ek = 0.18 J.

Answer: The mass of the oscillating body is 10.14 kg; potential energy at maximum displacement is 0.18 J.



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