$5\mathrm{.}3$ For the circuit below, use complex impedances to find the transfer function $I_1\frac{s}{V}(s).$

P$3.$ Electrostatic actuation is the most common type of actuation used for sensing applications. A lumped$-$model of spring$-$mass system is used to analyze the plate deflection under DC voltage. The governing equation is

$m{x}^{}+c{x}^{}+kx=F_{\text{e}\text{l}\text{e}\text{c}}$

$F_{\text{e}\text{l}\text{e}\text{c}}=\frac{A{V}^2}{2(g-x{)}^2}$

Where $A=1m{m}^2,k=1\frac{N}{m},=8\mathrm{.}85({10}^{-12})\frac{F}{m},g=1mm.$ For static analysis, any timedependent variables are set to zero. Using Matlab, $(1)$ find the static deflection x caused by $V=2$ volts; $(2)$ plot deflection $($x$)$ v$.$s$.$ V$.$