$2\mathrm{.}7$ Figure P$2\mathrm{.}7$ shows a two$-$mass translational mechanical system. The applied force fa$($t$)$ acts on mass m$1.$ Displacements z$1$ and z$2$ are absolute positions of masses m $1$ and m $2,$ respectively, measured relative to fixed coordinates $($the static equilibrium positions with $,fa(t)=0).$ An oil film with viscous friction coefficient b separates masses m $1$ and m $2.$ Derive the mathematical model of the mechanical system.

Figure P$2\mathrm{.}7$