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Figure shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated in the figure. The simple harmonic motion of the $x-$ projection of the radius vector of the rotating particle $P$ is
  • A$x = 2\,\cos \,\left( {2\pi t + \frac{\pi }{6}} \right)$
  • B$x = 2\,\sin \,\left( {2\pi t + \frac{\pi }{3}} \right)$
  • C$x = 2\,\sin \,\left( {2\pi t - \frac{\pi }{6}} \right)$
  • D$x = 2\,\cos \,\left( {2\pi t + \frac{\pi }{3}} \right)$
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