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A particle rotates in a clockwise motion according to the equation x=3cos(0.2t+0.813) what is its frequency?


Answer= [ ? ] hertz

Respuesta :

xero099

The particle has a frequency of 0.032 hertz.

The particle experiments a sinusoidal motion, whose mathematical model is described below:

[tex]x = x_{o} + A\cdot \cos (\omega\cdot t + \phi)[/tex] (1)

Where:

  • [tex]x[/tex] - Current position, in meters.
  • [tex]x_{o}[/tex] - Initial position, in meters.
  • [tex]\omega[/tex] - Angular frequency, in radians per second.
  • [tex]t[/tex] - Time, in seconds.
  • [tex]\phi[/tex] - Angle phase, in radians.

The frequency ([tex]f[/tex]), in hertz is defined by this formula:

[tex]f = \frac{\omega}{2\pi}[/tex] (2)

By direct observation on the formula described in statement we find that [tex]\omega = 0.2\,\frac{rad}{s}[/tex], then we find the frequency of the particle by (2):

[tex]f \approx 0.032\,hz[/tex]

The particle has a frequency of 0.032 hertz.

We kindly invite to check this question on simple harmonic motion: https://brainly.com/question/17315536

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