The weight on the spring makes 15 vibrations in one minute. Determine the weight of this weight

The weight on the spring makes 15 vibrations in one minute. Determine the weight of this weight if the spring rate is 9.86 N / m.

t = 1 min = 60 s.

N = 15.

k = 9.68 N / m.

m -?

The period of oscillation of a spring pendulum T is the time of one complete oscillation. The oscillation period T is determined by the formula: T = t / N, where t is the time during which the pendulum makes N complete oscillations.

T = t / N.

The period of the spring pendulum T is determined by the formula: T = 2 * P * √m / √k, where P is the number pi, which is 3.14, m is the mass of the load on the spring, k is the coefficient of spring stiffness.

t / N = 2 * P * √m / √k.

√m = t * √k / N * 2 * P.

m = t ^ 2 * k / N2 * 4 * P ^ 2.

m = (60 s) ^ 2 * 9.68 N / m / (15) ^ 2 * 4 * (3.14) ^ 2 = 3.9 kg.

Answer: a weight with a mass of m = 3.9 kg is attached to the spring.