What is the mass of a load oscillating on a spring whose stiffness is 0.25 kN / m if the load makes 40

What is the mass of a load oscillating on a spring whose stiffness is 0.25 kN / m if the load makes 40 vibrations in 32 seconds?

To calculate the value of the mass of the load attached to the taken spring, we apply the equality: t / n = T (period) = 2 * Π * √ (m / k) and m = k * t ^ 2 / (n ^ 2 * 4 * Π ^ 2).

Variables: k – rigidity of the taken spring (k = 0.25 kN / m = 250 N / m); t is the duration of the oscillations (t = 32 s); n is the number of vibrations (n = 40 vibrations).

Calculation: m = k * t ^ 2 / (n ^ 2 * 4 * Π ^ 2) = 250 * 32 ^ 2 / (40 ^ 2 * 4 * 3.14 ^ 2) = 4.06 kg.

Answer: Oscillations are performed by a load weighing 4.06 kg.