The structure shown is a retractable tool holder that is used in a factory to support a tool

at point $D.$ When the tool is to be used, the worker will grasp the tool and apply

a downward force to lower it to the position that is needed. When the tool is not in

use, the spring causes the tool to retract so that it is out of the way. The spring has $2$

$l\frac{b}{i}n.$ stiffness and assume $W$ is vertical.

If $W=16lb$ and the structure is to have an equilibrium configuration where $=65,$ determine the

unstretched length of the spring. $($Round the final answer to four decimal places.$)$

The unstretched length of the spring is

in$.$