Weight m = 0.2 kg suspended from a spring. performs N = 30 oscillations during t = 60 s.

Weight m = 0.2 kg suspended from a spring. performs N = 30 oscillations during t = 60 s. Determines the stiffness k of the spring.

m = 0.2 kg.

N = 30.

t = 60 s.

k -?

A load suspended on a spring is a spring-loaded pendulum that oscillates naturally.

The oscillation period of the spring pendulum T is expressed by the formulas: T = t / N and T = 2 * P * √m / √k, where t is the time during which the pendulum makes N oscillations, P is the number pi, m is the mass of the load suspended on the spring , k is the stiffness of the spring.

t / N = 2 * P * √m / √k.

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

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

k = 4 * (3.14) ^ 2 * 0.2 kg * (30) ^ 2 / (60 s) ^ 2 = 1.97 N / m.

Answer: the spring has a stiffness k = 1.97 N / m.