A $517$g$517\backslash ,\backslash$text$\{$g$\}517$g block is released from rest at height h$0$h$\_0$h$0$ above a vertical spring with spring constant k$=410$N$/$mk $=410\backslash ,\backslash$text$\{$N$/$m$\}$k$=410$N$/$m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring $11\mathrm{.}6$cm$11\mathrm{.}6\backslash ,\backslash$text$\{$cm$\}11\mathrm{.}6$cm$.$

$($a$)$ How much work is done $($a$)$ by the block on the spring and $($b$)$ by the spring on the block?

$($c$)$ What is the value of h$0$h$\_0$h$0?$

$($d$)$ If the block were released from height $3$h$03$h$\_03$h$0$ above the spring, what would be the maximum compression of the spring?.