a$.$ Derive the governing differential equations for this system.

b$.$ Obtain the transfer functions G$\_(1)($s$)=$x$\_(1)($s$)/($F$)($s$)$ and G$\_(2)($s$)=$x$\_(2)($s$)/($F$)($s$).$

c$.$ Assuming f$($t$)$F$($s$)=(1)/($s$)\backslash$Delta x$($s$)=$x$\_(1)($s$)-$x$\_(2)($s$).$

d$.$ Taking the parameters as m$=0\mathrm{.}01$kg$,$k$\_(1)=10($N$)/($m$),$k$\_(2)=100($N$)/($m$),$ and b$=0\mathrm{.}1$N$($s$)/($m$),$

use the step$($transfer function object$)$ command to plot $($separately$)$ the

responses of x$\_(1)($s$),$x$\_(2)($s$),$ and $\backslash$Delta x$($s$)$ to a unit step input.