F m J, r Motor k = k T b R www C When the rack is pulled back, it causes a pinion of radius r, which is directly connected to the motor's shaft, to rotate. The rotor or pulley, with combined inertia J and viscous damping b, is also affected. As a result, the motor's rotor is driven and generates a current i in the motor windings. To charge the capacitor, an RC circuit is employed. (A) Write the differential equations that link the force applied to the handle, F, with the voltage across the capacitor, ec. The motor constant and back electromotive force are equivalent but have different units. Express all equations solely in terms of the motor constant, K. Assume that the force between the rack and pinion is denoted by Frp. (B) When in J = 1, m = 1, r = 1, b = 1, C = 1, R = 1, and kt = kb = 1. Using the equations from part (A), derive the transfer function (force to voltage through circuit) for the system. Assume the units were kept consistent.