Please solve $17\mathrm{.}90$ a$)$ and b$)$ using Figure $17\mathrm{.}90.$

$17\mathrm{.}90$ A $6-$lb collar $C$ is attached to a spring and can slide on rodAB, which in turn can rotate in a horizontal plane. The mass moment of inertia of rodAB with respect to end $A$ is $0\mathrm{.}35lb*ft*s^2.$ The spring has a constant $k=15l\frac{b}{i}n.$ and an undeformed length of $10$ in $.$ At the instant shown, the velocity of the collar relative to the rod is zero and the assembly is rotating with an angular velocity of $12ra\frac{d}{s}.$ Neglecting the effect of friction, determine $($a$)$ the angular velocity of the assembly as the collar passes through a point located $7\mathrm{.}5$ in $.$ from end $A$ of the rod, $(b)$ the corresponding velocity of the collar

relative to the rod.