Determine the stiffness of the spring if a body weighing 2 kg vibrates at a frequency of 2 Hz.

The spring stiffness is calculated from the formula for calculating the oscillation frequency of a spring pendulum:

υ = 1 / 2Π * √ (k / m), where υ is the given frequency of oscillations of the spring (υ = 2 Hz), k is the required spring stiffness (N / m), m is the mass of the weight suspended from the spring (m = 2 kg ).

√ (k / m) = υ * 2Π.

k / m = (υ * 2Π) ^ 2.

k = (υ * 2Π) ^ 2 * m.

Let’s perform the calculation:

k = (2 * 2 * 3.14) ^ 2 * 2 = 315.51 N / m.

Answer: The spring rate is 315.51 N / m.