In the present study, elemental magnesium was reinforced with nano-size alumina particulates. Synthesis of materials was accomplished using the powder metallurgy route. Energy dissipation in the form of damping capacity was determined using free–free type suspended beam arrangement coupled with circle-fit approach. This technique is based on classical vibration theory, by which the geometry and material properties of the metallic specimen are related to measured resonant frequency and structural damping. Using the fact that the ratio of the vibration response to the applied force fits to a circle in the Argand plane for each resonant frequency of the test specimen, the damping factor and natural frequency is predicted accurately for the test specimen. The results revealed that an increase in the alumina content up to 0.4% volume percentage lead to an increase in the damping capacity up to 34%. Attempt is made to correlate the increase in damping with the various microstructural changes arising due to the presence of the nano-size alumina particulates in the composite sample.