Can u help me with c, d, and e?

u m ). A basic magnetic levitation scheme is illustrated in Figure 1. An electromagnetic coil, usually assumed to be xed to ground, may also have some motion, n43). It is desired to control the gap, my, between the coil and the mass, m, which may be a ferromagnetic material (or optionally a permanent magnet, PM). Magnetic levitation of a non-magnetic mass relies purel}r on the attractive force induced by variablereluctance effects. The total electromagnetic force can be modeled by a combined effect of a current-imluced force and a force due to the position of the permanent magnet. Fem : +052\": + Fpm(mg) " '. 9 W .5\". . due to If in Is current PM Suspended i- .' m " I I IEL'iS lU Magnetic m ux lines Figure 1: Form of magnetic levitation with gap 3:9 and drive current 2' as input. The ground may have motion with velocity -v,-(t). (a) Explain brieflyr how the state equations can be written, jty cm + v_,.(t) (1) Iii-m = _'F'cm/Tn + g (2) where Fm = Gig/1:3, where here it is assumed that if is an input (controlled) current, rather than V as shown in Figure 1. (h) Assume the mass is not a permanent magnet. Solve for the equilibrium conditions (I1:y(,,'UrrirJ! 20) (c) Linearize the state equations about the equilibrium condition and express the linear model as a standard 2nd order ODE (d) Express the model as a transfer function, :ry/i (0] Explain how would you change the model if a voltage, V, was the input as in Figure 1 rather than current