When a car hits a certain bump on the road, a shock absorber on the car is compressed a distance of $8$ in $.,$ then released $($see the following figure$).$

The shock absorber vibrates in damped harmonic motion with a frequency of $6$ cycles per second. The damping constant for this particular shock absorber is

$3\mathrm{.}5.$

$($a$)$ Find an equation that describes the displacement of the shock absorber from its rest position as a function of time. Take $t=0$ to be the instant that the

shock absorber is released. $($Let $f(t)$ be the displacement in inches after $t$ seconds, and assume that when $t=0$ the displacement is maximal.$)$

$f(t)=$

$($b$)$ How long does it take for the amplitude of the vibration to decrease to $0\mathrm{.}3$ in $.?($Round your answer to two decimal places.$)$