A disk cam is to be designed with reciprocating cylindrical follower such that the follower rises L$=16$ mm during the fist $240\backslash$deg of cam motion, then returns during the next $120\backslash$deg of cam motion. Using Simple Hormonic motion$($SHM$)$ for both rise and return, a$)$ Construct the cam displacement profile for $360\backslash$deg of cam rotation.

b$)$ Evaluate the first and second order kinematic coefficients for both rise and return stroke

c$)$ Calculate the maximum velocity and acceleration of the rise and return stroke if the cam rotates at $800$ rpm in clockwise direction.