solve please yourselfes not with ai $,$and handwritten.

Consider the following polishing mechine. The user push the machine forward with a force F in order to drive it with a velocty V$.$ Meanwhile, the motor of the machine generates a torque $T$ in onder to rotate the polishing roller with a torque with angular speed $.m_1$ is the mass of the cosina and the motor; $m_2$ is the mass of the roller. Io is the moment of inertia of the roller about its mass center O$.$ r is the raduis of the roller $.b$ is the viscous friction coefficient between the roller and polished surface.

a$)$ write the equetion that describes the dynamics of the system.

Hent: Draw, the FBD by showing necessary moments at harizontal forces

b$)$ Taking $f$ and $T$ as the inputs and $v$ as the output of the system. Draw the detailed block diagram.

c$)$ Draw the signal flow graph

d$)$ Find Transfer function with mason rule.