A body of mass m fell from a height h onto a spring balance pan. The mass of the cup is equal to M

A body of mass m fell from a height h onto a spring balance pan. The mass of the cup is equal to M, and the mass of the spring is negligible, the stiffness of the spring is k. Having adhered to the cup, the body begins to perform harmonic oscillations in the vertical direction. Find the amplitude of the vibrations and their energy.

The problem under consideration is focused on the use of a set of general physical rules, formulas and laws. In the presented task, it is necessary to use the law of conservation of momentum. With that said:

1) m * v1 = (M + m) * v;

2) v1 = √ (2 * g * h);

3) v = m * √ (2 * g * h) / (M + m);

The kinetic energy of bodies at the moment of impact is equal to the energy of the spring:

1) W = (M + m) * v² / 2 = m² * g * h / (M + m);

2) W = k * A² / 2.

Amplitude:

A = √ (2 * W / k).

Answer. The amplitude of the fluctuations will be k * A² / 2; the energy will be √ (2 * W / k).