In many applications, such as reading product codes in supermarkets and in printing and manufacturing, an optical scanner is utilized to read codes, as shown in Figure P2.42. As the mirror rotates, a friction force is developed that is proportional to its angular speed. The friction constant is equal to 0.06 N s/rad, and the moment of inertia is equal to 0.1 kg m2. The output variable is the velocity ω(t).
(a) Obtain the differential equation for the motor.
(b) Find the response of the system when the input motor torque is a unit step and the initial velocity at t = 0 is equal to 0.7.

Mirror Bar code MotorReflected light Laser Lens Detector Microcomputer FIGURE P2.42 Optical scanner.