The asymptotic Bode plot of the transfer function $${K \over {1 + {s \over a}}}$$. The error in phase angle and $$dB$$ gain at a frequency of $$\omega = 0.5a$$ are respectively

The function corresponding to the Bode plot of Figure, is

A unity feedback system with the open loop transfer function $$G\left( s \right) = {1 \over {s\left( {s + 2} \right)\left( {s + 4} \right)}}$$ has gain margin of ... $$dB.$$

An under damped second order system having a transfer function of the form $$M\left( s \right) = {{k\omega _n^2} \over {{s^2} + 2\zeta {\omega _n}s + \omega _n^2}}\,\,$$ has frequency response plot shown in Fig. below, then the system gain $$K$$ is __________ and the damping factor is approximately _______