What is the mass of a body fastened to a spring with a stiffness of K = 200 kN / m, if the period of its oscillations is T = 0.1 s

These tasks: k (the stiffness of the spring to which the body was attached) = 200 kN / m = 200 * 10 ^ 3 N / m; T (period of oscillation of the body on the spring) = 0.1 s.

The mass of a body can be determined from the formula for calculating the period of a spring pendulum: T = 2 * Π * √ (m / k), whence √ (m / k) = T / (2 * Π); m / k = T2 / 4Π ^ 2 and m = T ^ 2 * k / 4Π ^ 2.

Let’s calculate: m = 0.1 ^ 2 * 200 * 10 ^ 3 / (4 * 3.14 ^ 2) = 50.71 kg.

Answer: The mass of the body fastened to the spring is 50.71 kg