A $3-$lb collar is released from rest at point A and slides along a frictionless

inclined rod in a vertical plane while connected to a linear spring, as shown in Figure $3.$ The

stiffness of the spring is k $=4$ lb$/$ft and its unstretched length is $50$ in$.$

a$)$ Determine the speed vB of the collar when it reaches point B$.$

b$)$ Draw a free body diagram of the collar at B$.$ Calculate the force N exerted by the rod on the

collar and the acceleration a of the collar along the direction of the rod.

$($Figures given on the next page...$)$