Find the stiffness of the spring on which a weight of 4 kg is suspended, which makes 20 vibrations in 15 s.

m = 4 kg.

N = 20.

t = 15 s.

k -?

The period of any oscillatory movement T is the time during which the pendulum makes one complete oscillation. The period of the spring pendulum T is expressed by the formula: T = t / N, where N is the number of oscillations of the pendulum during time t.

The period of free natural oscillations of a spring pendulum T is expressed by another formula: T = 2 * P * √m / √k, where P is the number pi, m is the mass of the pendulum’s load, k is the stiffness of the spring to which the load is attached.

t / N = 2 * P * √m / √k.

√k = 2 * P * N * √m / t.

The spring stiffness of the pendulum k will be determined by the formula: k = 4 * P ^ 2 * N ^ 2 * m / t2.

k = 4 * (3.14) ^ 2 * (20) ^ 2 * 4 kg / (15 s) ^ 2 = 280.5 N / m.

Answer: the stiffness of the pendulum spring is k = 280.5 N / m.