A uniform string of length $l,$ constant density $$ and tension $T_0$ has its equilibrium position

along the x$-$axis, with end at $x=0$ fixed and the end at $x=l$ free to move $($in a plane$)$

perpendicular to the $x-$axis in such a way that the end of the string remains parallel to the

$x-$axis. If $u(x,t)$ is the transverse displacement of the string at a point $x$ and time $t>0,$

and released from rest while in the displaced position $u(x,0)=hx(l-x{)}^2,$ where $h>0$ is

small, find the subsequent motion of the string.