Write m$-$file$($s$)$ for the following tasks

$1)$ Obtain the unit$-$step response of a first order system analytically

$2)$ Create $3$ different first order systems where $\backslash (\backslash$mathrm$\{$T$\}1<mi>\backslash </mi>$mathrm$\{$T$\}2<mi>\backslash </mi>$mathrm$\{$T$\}3\backslash )$ and plot the unit step responses on the same plot. Then compare the response vs root location in the s$-$plane, which one responds faster?

$3)$ Using F$.$V$.$T$.$ calculate the steady$-$state error e$($t$)$ as $\backslash ($ t $\backslash$rightarrow $\backslash$infty $\backslash )$ for step input and verify with your plot

$4)$ Using F$.$V$.$T$.$ calculate the steady$-$state error $\backslash (\backslash$mathrm$\{$e$\}(\backslash$mathrm$\{$t$\})\backslash )$ as $\backslash (\backslash$mathrm$\{$t$\}\backslash$rightarrow $\backslash$infty $\backslash )$ for ramp input and verify with your plot