Damping Ratio Calculation

Q. The open loop transfer function G(s) of a unity feedback control system is given as,

G(s) = $\frac{K(s+\frac{2}{3})}{s^2(s+2)}$

From the root locus, it can be inferred that when k tends to positive infinity

1. Three roots with nearly equal real parts exist on the left half of the s-plane.
2. One real root is found on the right half of the s-plane
3. The root loci cross the j$\omega$ axis for a finite value of k : k $\ne$ 0.
4. Three real roots are found on the right half of the s-plane.

Q. A closed-loop system has the characteristic function ($s^2-4$) (s+1) + K(s-1) = 0. Its root locus plot against K is

1. 
2. 
3. 
4. 

Q. Consider a closed-loop system shown in Figure(A) below. the root locus for its is shown in Figure (B). the closed loop transfer function for the system is

1. $\frac{K}{1+(0.5s+1)(10s+1)}$
2. $\frac{K}{(s+2)(s+0.1)}$
3. $\frac{K}{1+K(0.5s+1)(10s+1)}$
4. $\frac{K}{K+0.2(0.5s+1)(10s+1)}$