Problem $3,10$pt

Problem $2\mathrm{.}9$ on reference book. In many mechanical positioning systems, there is

flexibility between one part of the system and another. The following figure depicts such a

situation, where a force $u$ is applied to the mass $M$ and another mass $m$ is connected to it$.$

The coupling between the objects is often modeled by a spring constant k with a damping

coefficient b $,$ although the actual situation is usually much more complicated than this.

$($a$)$ Write the equations of motion governing this system.

$($b$)$ Find the transfer function between the control input $u$ and the output $y.$