An engineer is designing a spring to be placed at the bottom of an elevator shaft. The total mass of the elevator and passengers is $M.$ If the elevator cable should break when the elevator is at a height $h$ above the top of the spring, calculate the value that the spring stiffness constant $k$ should have so that passengers undergo an acceleration of no more than $5\mathrm{.}0$ g when brought to rest.

$[18$ marks$]$