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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 on the figure.

Figure  shows the circular motion of a particle. The radius of the circle, the period, sense of revolution and the initial position are indicated on the figure. 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} \right )

(b)x(t)= B\sin \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}{2} \right )
 

Answers (1)

The answer is the option (a)x(t)= B\sin \left ( \frac{2\pi t}{30} \right )

Explanation: Circular motion is executed by P with radius B.

Here, x = OQ \cos (90^{\circ} - \theta)

                  =OQ \sin \theta

                  = B \sin \omega

Thus, \theta = \omega t

x = B \sin \frac{2 \pi }{T} t

x = B \sin \frac{2 \pi }{30}t

Thus, opt (a)

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