A $7\mathrm{.}5-$lb weight collar is released from rest in the position shown, sliding down an inclined rod. A spring installed at the end of the rod is used to stop the collar safely. If the coefficient of friction between the rod and the collar is $0\mathrm{.}15,$ determine:

$($a$)$ The maximum spring compression to stop the collar. $(10$ pts$)$

$($b$)$ The maximum downward speed of the collar. $(10$ pts$)$

$($c$)$ If the rod has negligible friction with the collar when the collar goes up the rod, what will be the maximum position the collar will reach before it starts to go down again? $(2$ pts$)$