Consider servomechanism. The control input is proportional to the voltage difference in the potentiometer, which in turn is proportional to the distance offset between the actual and desired position. Suppose the only forces acting on the platform to be moved are Fm, the force from the motor, and a frictional force Ff=10N which opposes that motion. We suppose Fm=10Vd where Vd is the voltage difference registered in the potentiometer. A motion of 1 m produces a voltage change of 0.1V via the feedback path. Suppose the mass of the platform is 1 kg, and the initial voltage difference is 2V.
(i) Write the equation for the acceleration as a function of the position change of the platform.
(ii) Sketch the general shape of the velocity function versus time.