$2103-213$ Homework: Kinematics of particles

The slotted arm $OA$ oscillates about $O$ within the limits shown and drives the crank $CP$ through the pin $P.$ For an interval of the motion, link $OA$ rotates with a constant angular velocity ${}^{}=K.$

$($a$)$ Show that the velocity and acceleration of pin $P$ are $v_p=2bK$ and $a_p=4b{K}^2.($Hint: Set $r-$ coordinates along the link $OA.)$

$($b$)$ Determine the acceleration of pin $P$ relative to the link $OA.$