Avery typical problem of electromechanical positioning control is an electric motor driving a load that has one dominant vibration mode. the problem arises in computer-disk-head control, reel-to-reel tape drives, and many other applications. a dc servo motor works by running current through a rotary toroidal armature coil which sits in a stationary magnetic field. as current is run through the coil, the induced magnetic field induces the rotor to turn. the torque developed is proportional to the current through the coil: t = ktia where t is the torque supplied to the shaft, ia is the current through the coil, and kt is the torque constant. the voltage drop across the motor is proportional to the motor’s velocity: vm = ke ˙θ where vm is the voltage drop across the motor, ke is a constant, and θ is the angular position of the shaft. the armature circuit also has resistance ra, inductance la, and input voltage va. the rotor has inertia j and the shaft viscous friction coefficient b.(a) find the equations of motion of this coupled electrical-mechanical system.(b) find the corresponding state space equations with the input va and load position as output θ.(c) assuming the voltage drop across the inductor is small enough to ignore, find the transfer function from the armature voltage input to the output speed of the load. what is the order of this system? for your !