For a unity feedback control system with the forward path transfer function

$$G(s) = {K \over {s\left( {s + 2} \right)}}$$

The peak resonant magnitude M_r of the closed-loop frequency response is 2. The corresponding value of the gain K (correct to two decimal places) is _________.

The Nyquist plot of the transfer function $$G(s) = {k \over {\left( {{s^2} + 2s + 2} \right)\left( {s + 2} \right)}}$$ does not encircle the point (-1+j0) for K = 10 but does encircle the point (-1+j0) for K = 100. Then the closed loop system (having unity gain feedback) is

A unity feedback control system is characterized by the open loop transfer function $$G(s) = {{10k\left( {s + 2} \right)} \over {\left( {{s^3} + 3{s^2} + 10} \right)}}$$ The Nyquist path and the corresponding Nyquist plot of g(s) are shown in the figures below. If 0 < K < 1, then number of poles of the closed loop transfer function that lie in the right half of the s-plane is

In the feedback system shown below $${\rm{G(s) = }}{1 \over {\left( {s + 1} \right)\left( {s + 2} \right)\left( {s + 3} \right)}}$$ The positive value of 𝑘 for which the gain margin of the loop is exactly 0 dB and the phase margin of the loop is exactly zero degree is ____