I need a hand written solution. Especially for the block diagram.

Thanks

$($a$)$ Figure $1$ shows a rigid link in which its free end is connected to a linear spring and a

linear damper. The length of the rigid link is L while the spring's constant and damping

coefficient are k and c$,$ respectively. To actuate this rigid link, we have mounted a motor at

its revolute joint and its moment of inertia at the joint is given as J$.$ The torque supplied by

the motor is given as tau while there is another horizontal force f which is applied at the centre

of the rigid link. Assuming zero initial conditions, derive and draw out the block diagram

components of this system in which the output of the system is the angular displacement

generated by the rigid link $($theta$).$ We can assume that theta is small and ignore gravity.

$(4$ marks$)$

$($b$)$ Determine the DC gain, natural frequency and damping ratio of the system.

$(3$ marks$)$

$($h$)$

ivioment or inertia or rig$$a $$nk

at the revolute joint is J

Fig. $1.$ A rigid link that can be actuated by a motor, which is placed at its revolute joint. $($a$)$

The configuration of the system in which the rigid link's length is L$.($b$)$ In addition to the

effects of the linear spring and damper, a horizontal force and the motor torque are affecting

the motions of the rigid link.