What is the mass of a load vibrating on a spring with a stiffness of 0.5 kN / m,

What is the mass of a load vibrating on a spring with a stiffness of 0.5 kN / m, if, with an amplitude of vibration of 6 cm, it has a maximum speed of 3 m / s.

1. It is known that moving bodies have kinetic and mechanical energy, which is equal to each other. Therefore:

E = mv ^ 2/2 -kinetic energy.

E = kA ^ 2/2 -mechanical energy.

mv ^ 2/2 = kA ^ 2/2.

m = kA ^ 2/2: v ^ 2/2 = kA ^ 2: v2 = 500 * (0.06: 3) ^ 2 = 500 * (0.0036: 9) ^ 2 = 500 * 0.0004 = 0.2.

We translate: 0.5 kN / m = 500 N / m. (in 1 kN / m 1000 N / m; 0.5 * 1000).

6 cm = 0.06 m. (In 1 m 100 cm; 6: 100 = 0.06).

Answer: 0.2 kg is the mass of a load oscillating on a spring.