Consider two masses $m_1$ and $m_2$ sitting on frictionless surfaces and attached to each other via a spring and damper, as shown above. The spring constant is $k$ and the damper constant is $b.$ There is an external force $F$ that can be applied to the mass $m_1$ as shown. Positive displacements $x_1$ and $x_2$ are to the right. Assume that when both $x_1=0$ and $x_2=0$ the spring is at its resting $($unstretched and uncompressed$)$ length. Which equations of motion describe the dynamics of the system?