The asymptotic Bode plot of a transfer function is shown in the figure. the transfer function G(s) corresponding to this bode plot is

Consider two transfer functions $${G_1}\left( s \right) = {1 \over {{s^2} + as + b}}$$ and $${G_2}\left( s \right) = {s \over {{s^2} + as + b}}.$$ The 3-dB bandwidths of their frequency responses are, respectively

The Nyquist plot of G(jω)H(jω) for a closed loop control system, passes through (-1,j0) point in the GH plane. The gain margin of the system in dB is equal to

Consider a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$ The value of 'a', so that the system has a phase-margin equal to $$\pi $$/4 is approximately equal to