A low speed constant angular velocity cam is to be designed such that the cam follower under goes the displacements as seen in the displacement diagram. The cam designer would like to use constant acceleration$/$constant deceleration profiles for all displacement rises and harmonic profiles for all displacement falls. Note that one entire rotation occurs in $6$ seconds.

Determine$/$Construct the following:

a$.$ The constant angular velocity of the cam in rpm

b$.$ The protocol for this follower with respect to time

c$.$ The displacement, velocity, and acceleration equations of the follower

d$.$ Graph of part $($c$)$ using Matlab. Be sure to use $$ in rad$/$s$.$ Use a three row subplot.