Question

The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the fig. $y$ - projection of the radius vector of rotating particle $P$ is :

• A. $y(t)$ = 3 cos ($\frac{3\pi\,t}{2}$) , where y in m
• B. $y(t)$ = 3 cos ($\frac{\pi\,t}{2}$) , where y in m
• C. $y(t)$ = 3cos2$\pi$ t , where y in m
• D. y(t) = 4 sin ($\frac{\pi\,t}{2}$) , where y in m

Answer 1

Answer: (B)

At t = 0, y displacement is maximum, so equation will be cosine function.
$ T =4s$
$ \omega = \frac{2\pi}{T} = \frac{2\pi}{4} = \frac{\pi}{2} rad /s $
$ y =a \cos\omega t $
$ y = 3\cos \frac{\pi}{2}t $