A spring $1\mathrm{.}50$ m long with force constant $\backslash (433\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )$ is hung from the ceiling of an elevator, and a block of mass $12\mathrm{.}8$ kg is attached to the bottom of the spring.

$($a$)$ By how much is the spring stretched when the block is slowly lowered to its equilibrium point? $($Enter the magnitude only.$)$

$-$ m

$($b$)$ If the elevator subsequently accelerates upward at $\backslash (1\mathrm{.}80\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ),$ what is the position of the block, taking the equilibrium position found in part $($a$)$ as $\backslash ($ y$=0\backslash )$ and upward as the positive $\backslash ($ y $\backslash )-$direction? $($Indicate the direction with the sign of your answer.$)$

$\backslash (\backslash$times $\backslash$mathrm$\{$m$\}\backslash )$

$($c$)$ If the elevator cable snaps during the acceleration, describe the subsequent motion of the block relative to the freely falling elevator. What is the amplitude of its motion?