$(5$ points$)$ A ball, starting from equilibrium, is pressed down with a hand against a linear ideal spring that is aligned vertically, as shown in the figure. When the hand no longer pushes doun, the ball is released from rest and flies upward. The ball reaches a maximum height of $2\mathrm{.}30$ meters above the equilibrium position of the spring and then falls back down, compressing the spring again. When answering the following questions do not ignore air resistance and use a system that consists of the ball, the spring, and the Earth $($but not the air or the hand$).$ Alr mesistance is a force that acts opposite the direction of the ball's motion.

$($a$)$ Use the descriptive sepirsentation $($vordo$)$ to describe the relevant energy transformations and transfers from the point the hand begins to push down on the ball all the way to the point when the ball recompresses the spring and is momentarily at rest.

$($b$)$ Do you expect the spring to compress the same distance when the ball comes back down as it originally did when the hand released the ball? Explain your reasoning.