# A 2.5 kg weight suspended on a spring makes 72 vibrations per minute. determine the stiffness of the spring.

m = 2.5 kg.

n = 72.

t = 1 min = 60 s.

k -?

The weight that is suspended by a spring is a spring-loaded pendulum. The period of oscillation of the pendulum is the time of one complete oscillation. Since the pendulum has made n oscillations in time t, then its period will be expressed by the formula: T = t / n.

The period T of free natural oscillations of a spring pendulum 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.

t / n = 2 * P * √m / √k.

√k = 2 * P * n * √m / t.

k = 4 * P2 * n2 * m / t ^ 2.

k = 4 * (3.14) 2 * (72) 2 * 2.5 kg / (60 s) ^ 2 = 142 N / m.

Answer: the spring has a stiffness k = 142 N / m.

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