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The radius of circle, the period of revolution, initial position and sense of revolution are indicated in the figure. X-projection of the radius vector of rotating particle P is

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$y (t) = 3 \cos (\frac{π t}{2}),$ where y in m

$y (t) = - 3 \cos 2 π t,$ where y in m

$y (t) = 4 \sin (\frac{π t}{2}),$ where y in m

$y (t) = 3 \sin (\frac{π t}{2}),$ where y in m

answer is D.

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Detailed Solution

Here T = 4s, A = 3 m

Time period T = $\frac{2 π}{ω} \Rightarrow 4 = \frac{2 π}{ω} \Rightarrow ω = \frac{π}{2}$

As the time is noted from the extreme position,

So, $y = Asin (ω t) \Rightarrow$

$y (t) = 3 \sin (\frac{π t}{2})$ , where y in m.

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