Problem $4.(3$ points$)$In this task you will match up frequency responses and Nyquist plots with one of the loop transfer functions shown below

a$.G_1(s)=\frac{k}{s+a}$

b$.$

c$.G_1(s)=\frac{k}{s+a}\frac{{}_0^2}{s^2+2{}_{0}s+{}_0^2}$

Firstly obtain which bode plot corresponds to and provide a justification of your choice

Secondly match it with corresponding Nyquist plot, and provide a justification with examples

Without justification and proofs, your choice is not acceptable.