The figure shows the circular motion of a particle. The radius of the circle,the period,the 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
  $x = 2\,\cos \left( {2\pi t + \frac{\pi }{3}} \right)$