The body performs harmonic oscillations with an amplitude of 0.1 m, a frequency of 2 Hz.

The body performs harmonic oscillations with an amplitude of 0.1 m, a frequency of 2 Hz. What is the mass of the body if the total energy of vibrations is 7.7 mJ.

The total energy of vibrations of the body W, J, can be found by the formula

W = 2 * n ^ 2 * m * A ^ 2 / T ^ 2,

where m is body weight, kg;

A – vibration amplitude, m;

T – oscillation period, s.

Frequency v, Hz, is a function inverse to the period, i.e.

v = 1 / T,

so we can write

W = 2 * n ^ 2 * m * A ^ 2 * v ^ 2,

whence the sought body mass is equal to

m = W / (2 * n ^ 2 * A ^ 2 * v ^ 2);

m = 0.0077 / (2 * 3.14 ^ 2 * 0.1 ^ 2 * 2 ^ 2) = 0.1 kg.

Answer: m = 0.1 kg = 100 g.