How does the coupled mass$-$spring$-$damper system, consisting of two masses and $m2)$ connected by springs $(k1,k2,k3)$ and dampers $(b1,b2),$ respond to a step input $(u(t))$ under the influence of gravity for each mass? Additionally, could you provide the free body diagrams for each mass, illustrating the forces and positions involved? Furthermore, derive the system's equations of motion in the form of differential equations and transfer functions, with a focus on representing the system dynamics concerning the positions of the masses. $|$