$(7)$ Two mass and spring problem: a mass $\backslash ($ m$\_\{1\}\backslash )$ is attached by a spring $($with spring constant $\backslash ($ k$\_\{1\}\backslash ))$ to a wall on its left; the first mass is attached to a second mass $\backslash ($ m$\_\{2\}\backslash )$ on its right by a second spring $($with spring constant $\backslash ($ k$\_\{2\}\backslash ))$; the second mass is attached to a dash pot on its right $($the "damping constant" of the dashpot is denoted by c$.)$ Let $\backslash ($ x$\_\{1\},$ x$\_\{2\}\backslash )$ denote the the displacments of mass one and mass two from their equilibrium postions.

$($a$)$ Wite down a system of second order DE that describes this situation.

$($b$)$ Suppose the dashpot is replaced by an external force $($acting simultaneonsly on both masses in the horizontal direction, and with magnitude $\backslash ($ f$($t$)\backslash )).$ Then write down a system of second order DE that desribe this situation.