Using the force$-$displacement graph shown determine: $($a$)$ The spring constant $($hint $-$ use values from the graph that exactly line up with gridlines$)($b$)$ The force required to compress the spring by $45$mm$,$ using the spring constant. $($c$)$ The work required to compress the spring by $45$mm$,$ using the spring constant. $($d$)$ If $0\mathrm{.}3888$W of power were used doing this, how long did it take? An object of $24$g is placed on top of the spring, and projected vertically once the spring released $($from being compressed by $45$mm $).($c$)$ To what height will the object rise $($neglecting air friction$)?$ Hint $-$ use the answer from par $($c$)$ and conservation of energy