A vertical spring$-$mass system undergoes damped oscillations due to air resistance. The spring constant is $2\mathrm{.}60104$ N$/$m and the mass at the end of the spring is $14\mathrm{.}1$ kg$.$

$($a$)$ If the damping coefficient is

b $=4\mathrm{.}50$ N $$ s$/$m$,$

what is the frequency of the oscillator?

Hz

$($b$)$ Determine the fractional decrease in the amplitude of the oscillation after $6$ cycles.