How does the coupled mass$-$spring$-$damper system, consisting of two masses $(m1$ and $m2)$ connected by springs $(k1,k2,k3)$ and dampers $($b$1,$ b$2),$ 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.

To assess the system's behavior, investigate a spectrum of parameter values within the specified ranges: $0\mathrm{.}5-5\frac{N}{m}$ for spring coefficients, $0\mathrm{.}5-5N\frac{s}{m}$ for damping coefficients, and $0\mathrm{.}5-2kg$ for masses. Selecting parameter combinations that encourage dynamic, vibrational patterns will lead to an oscillatory response, while opting for values that induce stability and damping will result in a non$-$oscillatory behavior. Adjusting these parameters provides a comprehensive exploration of the system's dynamics under varying conditions.