$($a$)$ A device consists of an object with a weight of $30\mathrm{.}0N$ hanging vertically from a spring with a spring constant of $240\frac{N}{m}.$ There

is negligible damping of the oscillating system. Applied to the system is a harmonic driving force of $13\mathrm{.}0Hz,$ which causes the

object to oscillate with an amplitude of $4\mathrm{.}00cm.$ What is the maximum value of the driving force $($in $N)?($Enter the magnitude.$)$

$($b$)$ What If$?$ The device is altered so that there is a damping coefficient of $b=5\mathrm{.}00N*\frac{s}{m}.$ The hanging weight and spring

constant remain the same. The same driving force as found in part $($a$)$ is applied with the same frequency. What is the new

amplitude $($in $cm)$ of oscillation?

$($c$)$ What If$?$ Repeat the same calculation as part $($b$),$ only now with a damping coefficient of $b=100N*\frac{s}{m}.($Enter the answer

in $cm.)$