This work aims at a better understanding of damping in coupled-cavities configurations such as liquid rocket engines (LRE). A cold flow rig called NPCC (New Pressurized Couple Cavities) is employed. It consists of two cavities mimicking dome and combustion chamber, linked by three injectors. The cavities can be either continuously excited or successively excited then relaxed by two different perforated rotating wheels placed at the outlets. Eigenmodes are first characterized. The rig is then excited at three successive eigenfrequencies using continuous modulation. The modes structures are checked using pressure transducers. Velocities at the injector's exits are measured with hot wires to characterize the injector's response. Forcing followed by relaxation (alternating forcing) is then used to study the damping rate of each mode, which is retrieved from the pressure transducers signal. 2D unsteady numerical simulations are performed to retrieve these values, both for continuous and alternating modulation. In the damping rate study, at least 10 excitation/relaxation cycles are necessary to achieve good convergence. The results are shown to be independant from the location of the probe used to derive the damping rate. The results are in reasonable agreement with the experiments for the three modes studied with continuous modulation. The study of the damping rate will however require 3D simulations to achieve good results with the methods presented here.