In a method for machining a workpiece, a cutting tool is guided relative to the workpiece, with a vibration being superposed, the amplitude of which is at least 5 μm. A supply circuit for a piezo actuator of a vibrating tool generates a voltage at the voltage output, which has a direct component and an alternating component. A supply system for a piezo actuator of a vibrating tool has the above-mentioned supply circuit which is connected to a secondary coil that is coupled to a primary coil.