For a feedback loop control system, a first order plus dead time $($FOPDT$)$ process with a process gain, $K_p=1,{}_p=1,$ and ${}_p=0\mathrm{.}5$ is under P$-$only control. Assuming $G_a(s)=1$ and $G_s(s)=1$;$1.$ Determine $K_C$ for cases $($a$)$ unstable system $($b$)$ sustained oscillations, $($c$)$ underdamped, $($d$)$ overdamped. $2.$ Using Cohen and Coon method to calculate $K_C$; What is the system dynamic behavior for this $K_C?$