$1-$ Consider the system shown in the figure below,

a$)$ Determine the value of $\backslash ($ k $\backslash )$ that yields a damping ratio $\backslash (\backslash$zeta $\backslash )$ of $0\mathrm{.}6.$

$(10$ points$)$

b$)$ Based on the numerical value found for $\backslash ($ k $\backslash )$ in part $($a$)$ of the problem, determine the open$-$loop gain and the system's type.

$(6$ points$)$

c$)$ Determine the steady$-$state errors for the system when it is subjected to

$1.$ a step reference input, $\backslash ($ r$($t$)=$A$\_\{0\}\backslash ).$

$2.$ a ramp reference input, $\backslash ($ r$($t$)=$A$\_\{1\}$ t $\backslash ).$

$(6$ points$)$

d$)$ Determine the settling time, $\backslash ($ T$\_\{$s$\}\backslash ),$ based on a $\backslash (2\backslash \%\backslash )$ criterion when the system is subjected to a unit$-$step input.

$(4$ points$)$