Because electro-magnetic actuators have both functionalities of actuation and sensing, they have potentials of sensorless vibration control as piezoelectric elements do. This paper discusses an implementation of a digital virtual impedance circuit with a R or RC circuit optimally designed by a theory of passive dynamic damper. The digital virtual impedance circuit, which consists of a computer and a controlled voltage source, can realize an arbitrary impedance. Using the virtual impedance concept, the optimally designed resistive component which might have negative value can be realized, even though conventional electro-magnetic shunt damping suffers from performance degradation.The experimental results demonstrate the effectiveness of the method.