Determine the stiffness of the spring if a weight of 100 g, swinging on it, made 40 vibrations in 20 seconds.

Task data: m (mass of the load swinging on a spring) = 100 g (0.1 kg); t (duration of rolling of the load on the spring) = 20 s; n (number of oscillations of the load) = 40 oscillations.

1) Determine the oscillation period: T = t / n = 20/40 = 0.5 s.

2) Let us express and calculate the stiffness of the spring: T = 2Π * √ (m / k), whence m / k = T ^ 2 / 4Π ^ 2 and k = 4Π ^ 2 * m / T ^ 2 = 4 * 3.14 ^ 2 * 0.1 / 0.5 ^ 2 ≈ 15.8 N / m.

Answer: The spring rate is 15.8 N / m.