It is possible to suspend a steel ball bearing by means of an electromagnet whose current is controlled by the position of the mass. A schematic of a possible setup is shown in the following figure. The equations of motion are mX mg f X I = + ( , ) where the force on the ball due to the electromagnet is given by f(X,I). It is found that the magnet force balances the gravity force when the magnet current is I0 and the ball at X0. If we write I= I0 + i and X = X0 + x and expand f about X = X0 and I= I0, and then neglect higher-order terms, we obtain a linear approximation mx k x k i = + 1 2 . Values measured for a particular device in the Stanford Controls Laboratory are m=0.02kg, k1=20N/m, k2=0.4N/A.