Summary: In this paper, we study the small noise behaviour of solutions of a non-linear second order Langevin equation \(\ddot{x}^{\varepsilon}_t+|\dot{x}^{\varepsilon}_t|^{\beta}=\dot{Z}^{\varepsilon}_{\varepsilon t}, \beta\in\mathbb{R} \), driven by symmetric non-Gaussian Lévy processes \(Z^{\varepsilon} \). This equation describes the dynamics of a one-degree-of-freedom mechanical system subject to non-linear friction and noisy vibrations. For a compound Poisson noise, the process \(x^{\varepsilon}\) on the macroscopic time scale \(t/\varepsilon\) has a natural interpretation as a non-linear filter which responds to each single jump of the driving process. We prove that a system driven by a general symmetric Lévy noise exhibits essentially the same asymptotic behaviour under the principal condition \(\alpha+2\beta<4\), where \(\alpha\in[0,2]\) is the “uniform” Blumenthal-Getoor index of the family \(\{Z^{\varepsilon}\}_{\varepsilon>0}\).