For the mass$-$spring$-$damper system from the problem for Topic $3$:

$($a$)$ Use Laplace Transforms to find an equivalent expression in the Laplace Domain. Assume the initial conditions are $\backslash ($ v$\_\{0\}\backslash )$ and $\backslash ($ x$\_\{0\}\backslash ).$

$($b$)$ Find a transfer function that relates the input, $\backslash ($ F$($s$)\backslash ),$ to the output, $\backslash ($ X$($s$)\backslash ).$

$($c$)$ What are the poles of this system? What do you know about the system from these poles?