About some methods in theory of damped oscillators

Ivana Kovacic

University of Novi Sad

Trg Dositeja Obradovica, 6, 21121, Novi Sad, Serbia

The present work is concerned with the response of one degree of freedom oscillatory systems which are under the influence of a significant linear damping force. The field method has been used to obtain motion of such systems when their parameters are constant or slowly vary in time. In both cases, first-order ordinary differential equations are derived for the modulation of the amplitudes and phases with damping and non-linearity. For some particular systems and some values of their parameters both analytical and numerical results are presented. The difference between them is negligible.

The applied algorithm of the field method appears to be straightforward and schematic, giving results with a satisfactory accuracy. The domain and the methodology of its application are widened, strengthening its powerfulness and generality.