Question $2[25$ marks$]$

riyure QL$-1$ A cam and follower system.

$($a$)$ Figure Q$2-1$ shows a cam and follower in their initial position, with the cam rotation angle $=0.$ Assume the follower can be represented by a vertical line at $x=0,$ that it can only move in the $y-$direction, and that it touches the cam at a single point $P$ at any time. The cam was designed such that the in the configuration shown, the radius $R$ varies as a function of the angle $$ according to the equation:

$R()=35+15cos(3),(EquationQ2-1)$

$($i$)$ Determine the minimum, maximum, and initial $y-$coordinate

$[4$ marks$]$

of point $P.$

$($ii$)$ Assuming an anti$-$clockwise rotational velocity of $=1$

$[8$ marks$]$

revolution per second, derive the equations for the $y-$velocity and $y-$acceleration of point $P$ as a function of time.

$($question continues on next page$)$

PTO

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