Question $5$

For a unity feedback system shown in Fig. $5,$

$($a$)$ For the system with $\backslash ($ K$=50\backslash ),$ judge the system stability by sketching the Nyquist diagram and using the Nyquist stability criterion.

$(10$ marks$)$

$($b$)$ For the same system in $($a$),$ judge the system stability by the Bode plot. Sketch the corresponding Bode plot in the semi$-$log graph in Appendix II$,$ and explain how the system stability is judged.

$(12$ marks$)$

$($c$)$ Judge the system stability when $\backslash ($ K$=5000\backslash ).$

$(3$ marks$)$