This paper studies the tuning process of controllers for fully actuated manipulators. To this end, we propose a methodology to design the desired damping matrix-alternatively, the derivative gain of a PD controller-of the closed-loop system such that n second-order systems can approximate its behavior with a prescribed damping coefficient, where n denotes the degrees of freedom of the system. The proposed approach is based on the linearization of the closed-loop system around the desired configuration and is suitable for different control approaches, such as PD control plus gravity compensation, impedance control, and passivity-based control. Furthermore, we extensively analyze simulations and experimental results in a cobot.