A $410$ g block is released from rest at height h$0$ above a vertical spring with spring constant k $=580$ N$/$m and negligible mass. The block sticks to the spring and momentarily stops after compressing the spring $12\mathrm{.}8$ cm$.$ 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$0?($d$)$ If the block were released from height $4\mathrm{.}00$ h$0$ above the spring, what would be the maximum compression of the spring?