Consider the circuit shown below.

Given

A$($s$)=($A$\_(0))/((1+($s$)/(\backslash$omega $\_(0)))^(2))$

Determine the closed$-$loop transfer function $($V$\_(0)($s$))/($V$\_($i$)($s$))$ in the form below

$($V$\_($o$)($s$))/($V$\_($i$)($s$))=($G$)/(($s$^(2))/(\backslash$omega $\_($p$)^(2))+($s$)/(\backslash$omega $\_($p$)$Q$\_($p$))+1)$

Here G is the dc gain

If n$=5$ and A$\_($o$)=1995,$ the value of Q$\_($p$)$ is

Consider the circuit shown below.

Given

A$($s$)=($A$\_(0))/((1+($s$)/(\backslash$omega $\_(0)))^(2))$

Determine the closed$-$loop transfer function $($V$\_($o$)($s$))/($V$\_($i$)($s$))$ in the form below

$($V$\_($o$)($s$))/($V$\_($i$)($s$))=($G$)/(($s$^(2))/(\backslash$omega $\_($p$)^(2))+($s$)/(\backslash$omega $\_($p$)$Q$\_($p$))+1)$

Here G is the dc gain

If n$=5$ and A$\_($o$)=1995,$ and $\backslash$omega $\_($p$)^(2)=$k$\backslash$omega $\_($o$)^(2),$ the value of $\text{'}$ k $\text{'}$ is