$(5$ points$)$ The figure below shows a mass$-$spring$-$damper system in series. The system's input is the force $u(t)$ applied on the second mass $m_2.$ The system has two outputs: the translational position $y_1(t)$ of the first mass $m_1$ and the translational position $y_2(t)$ of the second mass $m_2.$ Write a system of two differential equations relating the input $u(t)$ and the outputs $y_1(t)$ and $y_2(t).$