The oscillation period of the spring pendulum is T = 0.10 s. Determine the stiffness k

The oscillation period of the spring pendulum is T = 0.10 s. Determine the stiffness k of the spring if the mass of the load is m = 40g.

The oscillation period of a spring pendulum can be calculated using the formula:
T = 2Π * sqrt (m / k), where T is the period of oscillation of the spring pendulum (T = 0.1 s), m is the mass of the load (m = 40 g = 0.04 kg), k is the stiffness of the spring of the pendulum (N / m).
Let us express and calculate the spring stiffness of the pendulum:
sqrt (m / k) = T / 2Π.
m / k = (T / 2Π) ².
k = m / (T / 2Π) ² = 0.04 / ((0.1 / 2 * 3.14)) ² = 0.04 / (0.016) ² = 156.25 N / m
Answer: The spring rate of the pendulum is 156.25 N / m.