$($a$)$ Determine for each case below whether the given closed$-$loop specifications can be achieved by gain adjustment only and, if so$,$ the range$($s$)$ of K that achieve the specification. Explain any approximations. $($i$)$ In the step response, percent overshoot is between $4\mathrm{.}32\%$ and $16\mathrm{.}3\%$ while peak time is no greater than $2\mathrm{.}25$ seconds. $($ii$)$ In the step response, each transient term decays exponentially with time constant of $0\mathrm{.}5$ seconds. $($iii$)$ The frequency response has a resonant peak at approximately $15$ rad$/$sec$.($b$)$ Suppose a single$-$order, real$-$valued open$-$loop zero is introduced into the system; that is$,$ let G$($s$)=$ K$($s$$z$1)($s $+1)($s$+3)2$ for z$1$ in $($$,$$)$ Investigate the effect of this additional zero$$s placement on the Root$-$Locus. Which ranges of z$1$ most impact the closed loop system with respect to the properties investigated in parts $($a$)?($c$)$ Repeat parts $($a$)$ and $($b$)$ but in the case of a positive$-$unity$-$feedback configuration, or equivalently for gain K $0.$