Determine the vibration frequency and the coefficient of spring stiffness, at which a weight of 200 g

Determine the vibration frequency and the coefficient of spring stiffness, at which a weight of 200 g makes 60 vibrations in 2 minutes.

Data: m (weight of the cargo) = 200 g (0.2 kg); n (the number of vibrations made by the load) = 60 vibrations; t (oscillation time) = 2 min (120 s).

1) Determine the frequency of vibration of the load: ν = n / t = 60/120 = 0.5 Hz.

2) Period of fluctuations of the load: T = 1 / ν = t / n = 2 s.

3) Calculate the coefficient of spring stiffness: T = 2Π * √ (m / k), whence m / k = T2 / 4Π ^ 2 and k = 4Π ^ 2 * m / T2 = 4 * 3.14 ^ 2 * 0.2 / 2 ^ 2 = 1.97 N / m.

Answer: The oscillation frequency of the load is 0.5 Hz, and the spring rate is 1.97 N / m.