Determine the mass of a load vibrating on a spring with a stiffness of 100 h / m if it makes 300 vibrations in 60 seconds.

k = 100 N / m.

t = 60 s.

n = 300.

m -?

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

The period of a spring pendulum T is determined by the formula: T = 2 * п * √m / √k, where п is the number pi, m is the mass of the load, k is the stiffness of the spring.

t / n = 2 * п * √m / √k.

√m = t * √k / n * 2 * п.

We express the mass of the cargo m by the formula: m = t ^ 2 * k / n ^ 2 * 4 * п ^ 2.

m = (60 s) ^ 2 * 100 N / m / (300) ^ 2 * 4 * (3.14) ^ 2 = 0.1 kg.

Answer: the mass of the cargo is m = 0.1 kg.