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

mx$^()+$cx$^()+$kx$=$F$\_($elec$)$

F$\_($elec$)=(\backslash$epsi AV$^(2))/(2($g$-$x$)^(2))$

Where A$=1$mm$^(2),$k$=1($N$)/($m$),\backslash$epsi $=8\mathrm{.}85(10^(-12))($F$)/($m$),$g$=1$mm$.$ For static analysis, any time$-$

dependent 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$.$