Problem $4$: For the unity $($negative$)$ feedback system configuration with open loop transfer function $G(s)=\frac{K(s+3)}{s(s+2)},$ sketch the root locus showing sufficient details. Next, for the same configuration, assume that we add a new pole at $s=-a$ to the open loop transfer function $G(s).$ Can you $($without getting deep into the math$)$ qualitatively show how the root locus changes when $a=0,$ or $a=1,$ or $a=5($so$,$ there will be three plots you need to show$)?$ SHOW ALL WORK!