Damping using dry friction has long been recognized as an effective control method for many vibration problems. However, given the strong nonlinear nature of friction, the theoretical and experimental investigations of associated non-linear control methods are much more difficult than for linear control methods. Moreover, the difficulty of identifying friction models parameters for Limited Relative Displacement (LRD) contacts is still a subject of research. This study first proposes an identification procedure to evaluate the ability of the LuGre friction model to predict small amplitude (30 μm–150 μm) frictionally damped vibrations for a LRD contact. An experimental setup implementing an ideal frictionally damped Single Degree Of Freedom (SDOF) oscillator connected to an electrodynamic shaker is then presented to study friction damping. The simulation results are assessed against the experimental results, demonstrating that the identification procedure is well suited to estimate the parameters of the LuGre friction model and that the model captures very well the friction phenomenon for small amplitude vibrations.