Question $1$

The transfer function $V_c\frac{S}{V_s}(S)$ of the circuit in Figure $1$ where the inductor $L=0\mathrm{.}1H$ is given by

$\frac{V_c(s)}{V_s(s)}=\frac{d}{C(s^2+\text{e}\text{R}\text{s}+(\frac{f}{C}))}$

$($Please answer to $3$ decimal places, for example: $1\mathrm{.}543)$

$($i$)$ Find the values of $d=$

$(4$ marks$),$ e $=4$ marks$),f=(4$ marks$)$

$($ii$)$ Suppose $v_s(t)=u(t).$ Find the values of resistor $R$ and capacitor $C$ such that the step response of the capacitor voltage $v_c(t)$ is underdamped with complex poles $-70+-70j?$

$($Please answer to $3$ decimal places, for example: $1\mathrm{.}543)$

$R=$

$C=$

$(6$ marks$)$

$mF(7$ marks$)$