The body performs harmonic vibrations according to the law x = 0.2sin (4πt) Determine the vibration frequency.

The oscillation equation in general:

x = A * sin (w * t + φ0),

where A is the amplitude of the oscillations;

w is the cyclic vibration frequency;

ф – the initial phase of oscillations.

Comparing the given law of harmonic oscillations with the general law, we single out the value of the cyclic oscillation frequency:

w = 4p.

Frequency and cyclic frequency are related by the ratio

v = w / (2п).

Then the sought-for vibration frequency is

v = 4p / (2p) = 2.