The cycloidal displacement function for the rise function in the double dwell cam design is shown in the following figure.

Figure $1$ Cyclodial displacement function.

Suppose the rise is from $\frac{2}{3}$ to $,$ what is the value for $?(5$ points$)$

Assuming the total displacement $($rise$)$ is $h,$ list the boundary conditions $(s,v,a)$ for $=0$ and $=.(12$ points$)$

The acceleration function in $0$ is $a=2\frac{h}{{}^2}sin(2\frac{}{}),$ derive the velocity function. $(8$ points$)$

Given the angular velocity of the cam $=2ra\frac{d}{s},h=$ inch, what is the actual velocity and actual acceleration when $=\frac{}{8}?(10$ points$)$