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 a unity-gain feedback control system whose open-loop transfer function is G(s)=$${{as + 1} \over {{s^2}}}$$.

With the value of "a" set for phase-margin of $$\pi $$/4, the value of unit-impulse response of the open-loop system at t = 1 second 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

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