A $3\mathrm{.}00-$kg object is fastened to a light spring, with the intervening cord passing over a pulley. The pulley is frictionless, and its inertia may be neglected. The object is released from rest when the spring is unstretched.

The ends of a cord hang over the sides of a pulley attached to the ceiling. The left end of the cord is attached to the top of a vertical spring with spring constant k$.$ The bottom of the spring is attached to the flat ground. The right end of the cord is attached to a hanging spherical object with mass $3\mathrm{.}00$ kg$.$

$($a$)$ If the object drops $10\mathrm{.}7$ cm before stopping, find the spring constant of the spring.

N$/$m

$($b$)$ If the object drops $10\mathrm{.}7$ cm before stopping, find the speed of the object when it is $4\mathrm{.}30$ cm below its starting point.

m$/$s