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

A Bode magnitude plot for the transfer function $$𝐺(𝑠)$$ of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

Nyquist plots of two functions $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ are shown in figure.

Nyquist plot of the product of $${G_1}\left( s \right)$$ and $${G_2}\left( s \right)$$ is

The Bode plot of a transfer function $$G(s)$$ is shown in the figure below.

The gain is $$\left( {20\log \left| {G\left( s \right)} \right|} \right)$$ is $$32$$ $$dB$$ and $$–8$$ $$dB$$ at $$1$$ $$rad/s$$ and $$10$$ $$rad/s$$ respectively. The phase is negative for all $$\omega .$$ Then $$G(s)$$ is