A simplified model of an auto pilot of an aircraft is given by

\[
\mathrm{G}(s) \mathrm{H}(\mathrm{s})=\frac{\mathrm{K}(s+\alpha)}{s(s-\beta)\left(s^{2}+2 \xi \omega_{n} s+\omega_{n}^{2}ight)}
\]

Choose \(\alpha=\beta=1, \xi=0.5\) and \(\omega_{n}=4\). Sketch the root locus and find the range of gain \(\mathrm{K}\) for stability.