Given the following open$-$loop transfer function:

$G_{OL}=K_c(1+\frac{4}{s})(\frac{2}{0\mathrm{.}2s^2+0\mathrm{.}4s+1})$

a$.$ What is the characteristic equation for this system, in expanded form?

b$.$ Use the direct substitution method to determine the values of $K_c$ that make the system

closed$-$loop stable.

c$.$ According to your answer to Part b$,$ would $K_c=2$ result in a closed$-$loop stable or closed$-$

loop unstable response? Why?