A high precision electromechanical analog computer is described. The mechanical system is a torsion pendulum. Programmed torques provide an equation of motion which is identical to the equation:y″+f(x)y+g(x)=0. The solutions are obtained by recording the motion by means of a recording camera. The analog computer is used to study the betatron oscillations and the effects of resonances for the strong‐focusing Cornell synchrotron.