# Harmonic vibrations X are described by the equation x = 0.1cos (2πt-π / 4), m. Determine: the amplitude of the oscillations

**Harmonic vibrations X are described by the equation x = 0.1cos (2πt-π / 4), m. Determine: the amplitude of the oscillations, the cyclic frequency, the frequency of the oscillations, the period of the oscillations.**

In general, harmonic oscillations are described by the equation x = Xm * cos (ω * t + α),

where x is the instantaneous value, Xm is the amplitude value, (ω * t + α) is the oscillation phase, ω is the cyclic frequency, t is the time, α is the initial phase.

Comparing the equation with the conditions of the problem, with the equation of oscillations in the general case, we get that:

Amplitude of oscillations Xm = 0.1 (m);

Cyclic frequency ω = 2 * π = 2 * 3.14 = 6.28 (rad / s).

There is a relationship between the cyclic frequency (ω) and the frequency (f), which is described by the formula ω = 2 * π * f, from where we find the frequency f = ω / 2 * π = 2 * π / 2 * π = 1 (s-1) = 1 (Hz).

There is a relationship between the frequency and the period, which is described by the formula T = 1 / f, whence we find the period T = 1 / f = 1/1 = 1 (s).

Answer: Xm = 0.1 (m), ω = 6.28 (rad / s), f = 1 (Hz), T = 1 (s).