Problem $2(45$ point$)$

Consider the following feedback control system

Figure $1$: The feedback control system.

Suppose that the Bode plot $G(s)$ in Figure $1$ is given below

Solve the following problems:

$($i$)5$ point The transfer function of the above Bode plot is given below

$G(s)=\frac{C(s)}{U(s)}=\frac{k{}_n^2}{s^2+(20\mathrm{.}1{}_n)s+{}_n^2}$

Find the value of $k$ and ${}_n.$