$5.$ Below, you'll find a favourite assignment problem from one of Dr$.$ Vale's old professors. The plots on the bottom show the location of the poles as mapped into the complex plane; ignore the poles given in $(5)$ and $(7)$ and their associated curves $($b$)$ and $($d$).$ Hint: From the pole locations given in the complex plane, you can determine $\backslash (\backslash$zeta $\backslash )$ and $\backslash (\backslash$omega$\_\{$n$\}\backslash )$ or your value$($s$)$ of $\backslash (\backslash$tau $\backslash ),$ whichever is appropriate. Hint$2$: You should be able to figure out $(6)$ by process of elimination. Based on what you discovered in Q$1,$ does it make sense that the addition of a real, slow pole has this affect on the under$-$damped step response?

Example

Match up each step response with the corresponding pole$-$zero plot:

$(6).$