VDC LM IDC RM 1/B Tload T = kl Dc VEMF = kw Figure 1: DC motor equivalent circuit. Tload is a combination of the internal torque Tint (due to gear box) and the torque Text applied to wheel externally 1) Write the equation relating angular wheel frequency co and the encoder frequency fenc. That is, find the constant Kene such that co - Kenc*fene. You will need to review lecture slides in order to answer this question. 2) Assume that Voc and Inc are constant DC values and the wheel is rotating at constant angular frequency wo. Find an expression for motor parameter k as a function of VDC, IDC, RM and fenc. You may first solve in terms of co, and then use question 1 equation to put the answer in terms of fenc 3) Assume again that VDC and Inc are constant DC values. When a motor wheel is locked in place, the angular frequency of the motor is forced to zero, c = 0. Under these assumptions, redraw the equivalent circuit in Figure 1 and simplify as much as possible. Given VDC = 1 V, a DC current of Ipc = 0.5 A is measured. Calculate motor winding resistance RM-