A method is presented which can estimate the linear and non-linear damping parameters in a lightly damped system. Only a single response measurement from a free decay test is required as input. This ensures that the magnitude of the damping parameters is not compromised by phase distortion between measurements. The method uses the instantaneous energy to describe the long-term evolution of the system. Practically this is achieved by using only the peak amplitudes in each period. In this way the stiffness is effectively ignored, and only the damping forces are considered. For this reason, the method is not unlike the familiar decrement method, which can be used to estimate the linear damping in linear systems. The method is developed in the context of a weakly non-linear, lightly damping system, with both linear and cubic damping. Simulated response data is used to demonstrate the accuracy of the technique. The non-linear damping parameter is extracted from the response data to within 5% of the exact value, even though the non-linear term contributes less than 1% to the total force in the system.

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