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Figure shows the circular. motion of a particle. The radius of the circle, the period, sense of revolutionand 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) \( x=2 \cos \left(2 \pi t+\frac{\pi}{4}\right) \)
(b) \( x=2 \sin \left(2 \pi t+\frac{\pi}{4}\right) \)
(c) \( x=2 \sin \left(2 \pi t-\frac{\pi}{4}\right) \)
(d) \( x=2 \cos \left(2 \pi t-\frac{\pi}{4}\right) \)
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