If $$X = {\mathop{\rm Re}\nolimits} G\left( {j\omega } \right),\,\,$$ and $$y = {\rm I}mG\left( {j\omega } \right)$$ then for $$\omega \to {0^ + },\,\,$$ the Nyquist plot for $$G\left( s \right) = 1/\left[ {s\left( {s + 1} \right)\left( {s + 2} \right)} \right]$$

Consider the following Nyquist plots of loop transfer functions over $$\omega = 0$$ to $$\omega = \infty .$$ Which of these plots represents a stable closed loop system?

The Bode magnitude plot of $$H\left( {j\omega } \right) = {{{{10}^4}\left( {1 + j\,\omega } \right)} \over {\left( {10 + j\,\omega } \right){{\left( {100 + j\omega } \right)}^2}}}$$ is

If the compensated system shown in the figure has a phase margin of $${60^ \circ }$$ at the crossover frequency of $$1 rad/sec,$$ the value of the gain $$K$$ is