Problem $4.(10$ points $)$ Sketch the Bode Plot of the following transfer function. Label all slopes and asymptotes and points on the graph

$G(s)=\frac{100(s+4)}{(s^2+12s+20)(s+2)}$

a$.(4$ points$)$ Sketch the Bode plot

b$.(1$ points$)$ Gain margin $=$

c$.(1$ points$)$ Phase margin $=$

d$.(1$ points$)$ Access the stability. State the condition of stability

e$.(3$ points$)$ Draw the Nyquist and Mikhailov's plot