A unity negative feedback system has the open-loop transfer function $$$G\left(s\right)\;=\;\frac K{s\left(s\;+\;1\right)\left(s\;+\;3\right)}$$$ The value of the gain K (>0) at which the root locus crosses the imaginary axis is _________.

The open-loop transfer function of a plant in a unity feedback configuration is given as $$G\left(s\right)=\frac{K\left(s+4\right)}{\left(s+8\right)\left(s^2-9\right)}$$.The value of the gain K(>0) for which -1 + j2 lies on the root locus is __________________.

A plant transfer function is given as $$$G\left(s\right)=\left(K_p+\frac{K_1}s\right)\left(\frac1{s\left(s+2\right)}\right)$$$ . When the plant operates in a unity feedback configuration, the condition for the stability of the closed loop system is

The popular plot of the transfer function G(s)=$${{10\left( {s + 1} \right)} \over {\left( {s + 10} \right)}}$$ for $$0 \le \omega < \infty $$ will be in the