A $10-$lb weight is suspended by a spring that is stretched $2$ inches by the weight. Assume a resistance whose magnitude is $\frac{40}{\sqrt[\phantom{2}]{g}}$ times

the instantaneous velocity in feet per second. If the weight is pulled down $6$ inches below its equilibrium position and released, find the

time required to reach the equilibrium position for the first time.

The weight reaches the equilibrium position for the first time seconds after it is released.

$($Do not round until the final answer. Then round to the nearest thousandth as needed.$)$