Please solve this without matlab part $($c $)$

Problem $1(30$ pts$)$:

Consider a linear mechanical system where a force $u$ is applied to the mass $M$ and another mass

$m$ is connected to it$.y$ and $x$ are the displacements of these respective masses. The coupling

between the objects is modeled by a spring constant $k$ and a damper with damping coefficient $b.$

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

$($b$)$ Find a state$-$space model of this system with the states being the displacement and velocities

of masses $m$ and $M.$

$($c$)$ Assuming all coefficients are $1$ for simplicity. Find the transfer function between the control

input $u$ and the output $y.$

Hint: You can validate your answers using MATLAB.