Problem $9.$ Consider the mechanical model of a

printer. The printer head of mass $m$ at position $x$ is

driven by an elastic belt whose segments have

stiffness $2k,2k,$ and $k.$ The drums have radius $R,$

angle ${}_1,{}_2,$ mass $m_1,m_2,$ and mass moment of

inertia $J_1=\frac{1}{2}{m}_1{R}^2,J_2=\frac{1}{2}{m}_2{R}^2$ about their centers.

The left drum is driven by a torque $M.$

a$)$ Determine the DoF and derive the EoM for $x,{}_1,$

and ${}_2$ using FBD and FLD$.$