(Solved): For the following system shown, a. Draw the necessary free-body diagram and derive the differentia ...

For the following system shown, a. Draw the necessary free-body diagram and derive the differential equation of motion b. Using the differential equation obtained in Part (a), determine the transfer function. Assume initial conditions $x(0)=0$ and $\stackrel{?}{x}(0)=0$. c. Using the differential equation obtained in Part (a), determine the state-space representation.