In this paper,a damped motion is taken as an illustrative example to study the characteristics of inverse problem of dynamics and inverse problem of variational calculus and the relation between the two. First, from a special equation of damped motion, four differential equations of motion, i.e. four different functions of force are obtained, the connections and the differences among them are discussed. Secondly, the corresponding Lagrangians and a family of Lagrangians are constructed directly from the two among the four above equations. Finally, new result of the combination of the two inverse problems is pointed.