Question $3$: A cam with a minimum radius of $32$ mm is to be designed for a knife$-$edge follower with the following data:

$$ To raise the follower through $35$ mm during $120$ rotation of the cam

$$ Dwell for next $55$ of the cam rotation

$$ Descending of the follower during the next $110$ of the cam rotation

$$ Dwell during the rest of the cam rotation

Draw the profile of the cam if the ascending and descending of the cam is with simple harmonic motion and the line of stroke of the follow is offset $10$ mm from the axis of the camshaft.

What is the maximum velocity and acceleration of the follower during the ascent and the descent if the cam rotated at $150$ rpm$?$