$5.$ Consider the system above.

$($a$)$ Is the system stable for $\backslash ($ K$=1\backslash )?$ Argue using any method. $(8$ points$)$

$($b$)$ What is the gain and phase margin for the system when $\backslash ($ K$=1\backslash )?(6$ points$)$

$($c$)$ For what range of positive gains $\backslash ($ K$>0\backslash )($if any$)$ is the closed$-$loop system stable? $(6$ points$)$