Determine the stiffness of the spring to which is attached a body weighing 30 g and performing

Determine the stiffness of the spring to which is attached a body weighing 30 g and performing 300 vibrations in 2 minutes.

Given: m (mass of the body attached to the spring) = 30 g (0.03 kg); t (body vibration time) = 2 min (120 s); n (number of vibrations) = 300 vibrations.

The spring stiffness can be calculated from the formulas for calculating the oscillation period of the body attached to it: T = t / n = 2Π * √ (m / k), whence k = 4Π ^ 2 * m * n ^ 2 / t ^ 2.

Let’s calculate the stiffness of the spring: k = 4 * 3.14 ^ 2 * 0.03 * 300 ^ 2/120 ^ 2 ≈ 7.4 N / m.

Answer: The spring rate is 7.4 N / m.