A compact object with a mass of $5\mathrm{.}60$ kg oscillates at the end of a vertical spring with a spring constant of $1\mathrm{.}80104$ N$/$m$.$ The motion is damped by air resistance, and the damping coefficient is b $=3\mathrm{.}00$ N $$ s$/$m$.$

$($a$)$

What is the frequency $($in Hz$)$ of the damped oscillation?

$($b$)$

By what percentage does the amplitude of the oscillation decrease in each cycle?