This paper describes the design and the performance analysis of an $H_2$ controller for noncollocated active vibrating systems. An experiment for the active vibration control of a flexible structure is performed. The experimental model used is a cantilever beam controlled by an active damping system consisting of a laser sensor and an electromagnetic actuator. The $H_2$ controller design is based on the reduced order model and the designed system is capable of attenuating vibration without causing spillover instability. The design procedure to prevent spillover instability is described via the sensitivity analysis. The performances of the controller are verified by experimental results.