Follower displacement function: Design a displacement function.

The follower must:

Dwell at $y=2cm$ for $90$

Rise $3$ cm for $45$ with continuous velocity

Dwell at $y=5cm$ from $135$ to $225$

Return $($fall$)$ to $y=2cm$ from $225$ to $270$ with continuous displacement

Dwell for the remaining $90$ of cam rotation.

a$.$ Write the boundary conditions and choose the degree of the polynomial to satisfy them.

Solve for the coefficients of the polynomial for the rise. $(10$ Points$)$

b$.$ Write the boundary conditions and choose the degree of the polynomial to satisfy them.

Solve for the coefficients of the polynomial for the return. $(10$ Points$)$

c$.$ Write the equations of $y=y()$ for each section of the displacement function. $(10$ Points$)$

d$.$ Write the equations of the velocity, acceleration and jerk as a function of $$ and the consta angular velocity of the cam, $.(10$ Points$)$

e$.$ Plot the displacement, velocity, acceleration, and jerk functions $($with hand$).(10$ Points$)$