Find the mass of the load that is on the spring with a stiffness of 250 N \ m. At the same time, he makes 20

Find the mass of the load that is on the spring with a stiffness of 250 N \ m. At the same time, he makes 20 vibrations in 16 seconds.

k = 250 N / m.

N = 20.

t = 16 s.

m -?

The weight attached to the spring is a spring-loaded pendulum. For a spring pendulum, the time of one complete free oscillation T is determined by the 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.

The time of one complete oscillation is called the period T and is determined by the formula: T = t / N, where t is the time during which N oscillations are completed.

2 * P * √m / √k = t / N.

√m = t * √k / N * 2 * P.

The mass of the cargo will be determined by the formula: m = t ^ 2 * k / N ^ 2 * 4 * P ^ 2.

m = (16 s) ^ 2 * 250 N / m / (20) ^ 2 * 4 * (3.14) ^ 2 = 4 kg.

Answer: the load has a mass of m = 4 kg.