What stiffness should a spring be taken so that a weight of 0.1 kg would make 10 vibrations in 3 s?

Data: m is the mass of the vibrating load (m = 0.1 kg); n is the number of perfect vibrations (n = 10 pcs.); t is the duration of the oscillations (t = 3 s).

To find out the stiffness that the taken spring should have, consider the equality: t / n = T (period) = 2 * Π * √ (m / kx), whence we express: m / kx = t ^ 2 / (n ^ 2 * 2 ^ 2 * Π ^ 2) and kx = m * n ^ 2 * 2 ^ 2 * Π ^ 2 / t ^ 2.

Let’s perform the calculation: kx = m * n ^ 2 * 2 ^ 2 * Π ^ 2 / t ^ 2 = 0.1 * 10 ^ 2 * 2 ^ 2 * 3.14 ^ 2/3 ^ 2 ≈ 43.82 N / m.

Answer: The taken spring must have a stiffness of 43.82 N / m.