Determine the mass of a body suspended on a spring with a stiffness of k = 25N / m, if it makes 25 vibrations in 1 minute.

k = 25 N / m.

t = 1 min = 60 s.

N = 25.

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 oscillations.

For a spring pendulum, the period of its natural free oscillations T is expressed by another formula: T = 2 * P * √m / √k, where P is the number pi, m is the mass of the load, k is the stiffness of the spring.

t / N = 2 * P * √m / √k.

√m = t * √k / N * 2 P.

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

m = (60 s) ^ 2 * 25 N / m / (25) ^ 2 * 4 * (3.14) ^ 2 = 3.65 kg.

Answer: the load has a mass m = 3.65 kg.