A unity feedback system has the forward loop transfer function $$G\left( s \right) = {{K{{\left( {s + 2} \right)}^2}} \over {{s^2}\left( {s - 1} \right)}}$$

(a) Determine the range of $$K$$ for stable operation

(b) Determine the imaginary axis crossover points

(c) Without calculating the real axis break - away points, sketch the form of root loci for the system.

The system having the Bode magnitude plot shown in Fig. below has the transfer function

Which of the following is the transfer function of a system having the Nyquist plot shown in Fig. below.

An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\,\,$$ has frequency response plot shown in Fig. below, then the system gain $$K$$ is __________ and the damping factor is approximately _______