$(10$ points$).$ Draw the free$-$body diagram for each mass and write the ordinary differential equations $($ODEs$)$ of the dynamic system assuming that the initial conditions are zero.

$(15$ points$).$ Obtain the transfer functions $\frac{x_1(s)}{U(s)}$ and $\frac{x_2(s)}{U(s)}$ of the translational mechanical system where $x_1(t)$ and $x_2(t)$ are the displacement of the masses $m_1$ and $m_2,$ respectively, and $u(t)$ is the external force applied to the system.