It is widely accepted that the non-turbulent perturbations in modern telescopes arise from the instrumentation systems, such as fans and cooling pumps, and from the mechanical vibrations induced by the wind or the telescope tracking. In order to develop a properly control law to mitigate the vibrations effects, an accurate model of all the mechanical vibrations is needed. In this paper, we model these vibrations as a sum of continuos-time damped oscillators (the equivalent transfer function of discrete-time autoregressive second-order models) and we estimate the oscillators parameters from discrete-time data based on Maximum Likelihood method. Finally, we utilize our proposed method to estimate the vibrations frequency peaks at the LBTO.