Assume that the coupling between the motor and the inertial load of the proceding problem is flexible (e.g., a long shaft). This can be modeled by adding a torsional spring between the motor inertia and the load inertia. Now we can no longer lump the two inertias and damping coefficients as if they were one, but we need to write separate equations for the two inertias. In total, there will be three equations in this system:

1. the motor electrical equation

2. the motor mechanical equation (Jm and Bm)

3. the load mechanical equation (J and B)

a. Sketch a diagram of the system.

b. Use free-body diagrams to write each of the two mechanical equations. Set up the equations in matrix form.

c. Compute the transfer function from input voltage to load inertia speed using the method of determinants.