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(D) From the figure,the radius of the circle is $A = 3 \ m$ and the time period is $T = 4 \ s$.The angular velocity is given by $\omega = \frac{2 \pi}

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$y(t)=3 \cos \left(\frac{\pi t}{2}\right),$ where $y$ is in $m$

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(D) From the figure,the radius of the circle is $A = 3 \ m$ and the time period is $T = 4 \ s$.The angular velocity is given by $\omega = \frac{2 \pi}{T} = \frac{2 \pi}{4} = \frac{\pi}{2} \ rad/s$.At $t = 0$,the particle $P$ is at the positive $y$-axis,which means its position vector makes an angle $\phi = \frac{\pi}{2}$ with the positive $x$-axis.The $y$-coordinate of the particle at any time $t$ is given by $y(t) = A \sin(\omega t + \phi)$.Substituting the values,$y(t) = 3 \sin\left(\frac{\pi t}{2} + \frac{\pi}{2}ight)$.Using the trigonometric identity $\sin(	heta + \frac{\pi}{2}) = \cos 	heta$,we get $y(t) = 3 \cos\left(\frac{\pi t}{2}ight)$.

List-$I$	List-$II$
$A$. $\sin^2 \omega t$	$I$. Periodic but not $SHM$ $(T = 2\pi/\omega)$
$B$. $\sin^3 \omega t$	$II$. Periodic but not $SHM$ $(T = \pi/\omega)$
$C$. $\sin \omega t + \cos \pi \omega t$	$III$. Non-periodic
$D$. $\cos \omega t + \cos 2\omega t$	$IV$. Periodic but not $SHM$ $(T = 2\pi/\omega)$

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

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