A $330$g$330\backslash ,\backslash$text$\{$g$\}330$g block is dropped onto a relaxed vertical spring that has a spring constant of k$=4\mathrm{.}3$N$/$cmk $=4\mathrm{.}3\backslash ,\backslash$text$\{$N$/$cm$\}$k$=4\mathrm{.}3$N$/$cm$.$ The block becomes attached to the spring and compresses the spring $13$cm$13\backslash ,\backslash$text$\{$cm$\}13$cm before momentarily stopping.

While the spring is being compressed:

$($a$)$ What work is done on the block by the gravitational force?

$($b$)$ What work is done on the block by the spring force?

$($c$)$ What is the speed of the block just before it hits the spring?

$($d$)$ If the speed at impact is doubled, what is the maximum compression of the spring?