A person drops a vertically$-$oriented, cylindrical steel bar from a height of $1\mathrm{.}00$ m $($measured from the floor to the bottom of the bar$).$ The bar has length $L=0\mathrm{.}80m,$ radius $R=0\mathrm{.}50cm,$ mass $m=1\mathrm{.}40kg,$ and Young's modulus $Y=1\mathrm{.}90{10}^{11}Pa.$ The bar hits the floor and bounces back up$,$ maintaining its vertical orientation.

Use the gravitational acceleration $g=9\mathrm{.}81\frac{m}{s^2}.$ Assume that the collision with the floor is elastic, and that no rotation occurs.

What is the maximum compression $l$ of the bar?