A spring $1\mathrm{.}50$ m long with force constant $417$ N$/$m is hung from the ceiling of an elevator, and a block of mass $13\mathrm{.}7$ 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 $1\mathrm{.}77$ m$/$s$2,$ what is the position of the block, taking the equilibrium position found in part $($a$)$ as y $=0$ and upwards as the positive y$-$direction. $($Indicate the direction with the sign of your answer.$)$

m

$($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?

m