The figure shows the circular motion of a particle. The radius of the circle is $B$,the period is $30 \ s$,the sense of revolution is clockwise,and the initial position at $t = 0$ is at an angle of $45^\circ$ (or $\pi/4$ radians) with the positive $y$-axis in the first quadrant. The simple harmonic motion of the $x$-projection of the radius vector of the rotating particle $P$ is:

• A
  $x(t) = B \sin \left( \frac{2\pi t}{30} + \frac{\pi}{4} \right)$
• B
  $x(t) = B \cos \left( \frac{\pi t}{15} \right)$
• C
  $x(t) = B \sin \left( \frac{\pi t}{15} + \frac{\pi}{2} \right)$
• D
  $x(t) = B \cos \left( \frac{\pi t}{15} + \frac{\pi}{4} \right)$