$5.$ A mass attached to a spring slides on a surface having the values m$=2$ lb$-$s$2/$in$,$ k $=800$ lb$/$in$,$and $\backslash$mu k $=0\mathrm{.}1.$ The initial displacement is $1\mathrm{.}2$ in$.$and the initial velocity is zero.

Calculate:

$($a$)$ The decay per cycle

$($b$)$ The number of half cycles until the oscillation stops.