The Nyquist plot given by MATLAB for a certain system with $K=1$ is shown in Figure $1.$ Note that the Nyquist plot has an asymptote at the line $Re\{z\}=0\mathrm{.}064.$ The left part of Figure $1$ shows the "full" Nyquist plot, while a close$-$up view is shown on the right side of Figure $1.$ It is known that the uncompensated system has no poles outside the unit circle.

$($A$)$ Find the gain margin and the phase margin for the system. Estimate the range of $K>0$ for which the closed$-$loop system is stable. $[10$ points$]$

$($B$)$ Sketch a possible root locus for this system. $[10$ points$]$

$($C$)$ Sketch the Bode magnitude and Bode phase plots for this system. Clearly label any specific points on the Bode plots that the frequency response must go through. For example, if you can calculate the de gain, label it on the Bode plots. $[10$ points$]$

Figure $1$: Nyquist Plot for Problem $1.$