Problem $10(7$ pts$.)$:

a$)(4$ pts$.)$ Draw a negative feedback system with the direct path block with transfer function $G_1(s)=\frac{5}{s-2}$ and with the feedback path block with transfer function $G_2(s)=\frac{K}{s+4}.$

Calculate the overall transfer function of the feedback loop.

b$)(3$ pts$)$ Determine the value of K for the system to have an underdamped behavior.

FORMULAS:

$\backslash$table$[[$Basic Laplace transforms,Basic Laplace properties$],[$f$($t$),),f(t),$F$($s$)],[1(t)$ or $u(t),\frac{1}{c^{\text{'}}},k_1{f}_1(t)+k_2{f}_2(t),k_1{F}_1(s)+k_2{F}_2(s)$