The numerical solution of dynamic problems often results spurious oscillations. In order to eliminate them, a damping effect must be included in the numerical scheme. However, the concrete shape of the damping characteristics has a great importance in the efficiency of oscillation reduction. In this article, a novel approach has been introduced with adjustable damping character. The damping effect is exerted as viscous damping according to the formulation of Caughey damping. Using the proposed method, a wide range of damping curves can be approximated with high accuracy. The newly developed method is mainly useful for contact-impact and wave propagation problems.