$2$nd Order Systems Review: Obtain the free response of the following model:

$2$x$\text{'}\text{'}+10$x$\text{'}+8$x $=$ f$($t$)$

for the following three cases:

a$.$ x$(0)=2,$ x$\text{'}(0)=5$

b$.$ x$(0)=2,$ x$\text{'}(0)=-5$

c$.$ x$(0)=2,$ x$\text{'}(0)=0$

You should demonstrate your ability to solve this problem by hand, by providing reasonable detail showing how you get X$($s$)($after partial fraction expansion$)$ and x$($t$).$ Plot each case $($you may use Matlab or a similar package to do this$)-$ PLOT ALL $3$ ON THE SAME PLOT