A system and method are provided for damping a vibrating surface, such as a drumhead, of a percussion instrument by attaching a patch made from a viscoelastic urethane polymer to an exterior face of the vibrating surface. Such a patch has a self-adhesive quality and may be attached by contacting the vibrating surface. In one embodiment, the patch has a tapered edge that serves to improve the quality of the bond between the patch and the surface.