Find the mass of the load that, on a spring with a stiffness of 250 N / m, makes 20 vibrations in 16 s.

1. Let’s write an expression to determine the period of oscillation of a load on a spring:
T = 2π * √ (m / k), where m is the mass of the load, k is a coefficient showing the stiffness of the spring.
2. The period of oscillation is such a period of time during which the body returns to the same point from which it began its movement.
T = t / n, where n is the number of oscillations, t is the time during which the body made these oscillations.
3. Equate and square both sides:
t / n = 2π * √ (m / k)
(t / n) ² = 4π² * m / k
4. Let us express the mass of the cargo from this expression:
m = t² * k / (4π² * n²)
5. Substitute the numerical values ​​and find the mass of the cargo:
m = t² * k / (4π² * n²) = 16² * 250 / (4π²20²) = 4.06 kg.

Answer: the mass of the load on the spring is 4.06 kg.