  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 L\'evy 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 L\'evy 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
$\{Z^\varepsilon\}_{\varepsilon>0}$.
