The transfer function of a system is $${{Y\left( s \right)} \over {R\left( s \right)}} = {s \over {s + 2}}.$$ The steady state $$y(t)$$ is $$Acos$$$$\left( {2t + \phi } \right)$$ for the input $$\cos \left( {2t} \right).$$ The values of $$A$$ and $$\phi ,$$ respectively are

The phase cross-over frequency of the transfer function $$G\left( s \right) = {{100} \over {{{\left( {s + 1} \right)}^3}}}\,\,$$ in $$rad/s$$ is

Consider the following asymptotic Bode magnitude plot ($${\omega \,\,}$$ is in $$rad/s$$)

Which one of the following transfer functions is best represented by the above Bode magnitude plot?

Loop transfer function of a feedback system is $$G\left( s \right)H\left( s \right) = {{s + 3} \over {{s^2}\left( {s - 3} \right)}}.$$ Take the Nyquist contour in the clockwise direction. Then, the Nyquist plot of $$G(s)$$ $$H(s)$$ encircles $$-1+j0$$