question_answer 33)

                  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) \[x(t)=B\cos \left( \frac{\pi t}{15} \right)\] (c) \[x(t)=B\sin \left( \frac{\pi t}{15}+\frac{\pi }{2} \right)\] (d) \[x(t)=B\cos \left( \frac{\pi t}{15}+\,\frac{\pi }{2} \right)\]

Answer:

                  (a) \[\frac{x(t)}{B}\,=\,\sin \,\omega t\]                 \[x(t)=B\sin \,\omega t\]                                 \[=\,B\,\sin \,\left( \frac{2\pi }{T}t \right)\]                 \[=\,B\,\sin \,\left( \frac{2\pi }{30}t \right)\]