On the basis of the results of a previous article, it has been obtained an approximate explicit expression of the lagrangian parameters and their time-derivatives with errors of order . All that has been achieved for a mechanical system possessing two degrees of freedom and subjected to slowly time-variable constraints.
In this paper the problem of the small oscillations of a mechanical or electric system, with two degrees of freedom and some of the involved parameters slowly varying with time, is analysed. An approximate solution, valid in a vary large time interval,is obtained.
An approximate method of integration for some differential equations in non-linear optics developed by Graffi has been here extended to the propagation in an absorbing non linear medium.
The Author exposes some applications of the results of the first note, in particular to the double pendulum.
The author considers the differential equation: where is a small number. He finds an approximate solution of (1) with an error , when , and with an error when . He exposes some applications of his results to a problem of mechanics.
The Author gives a simple proof for the approximate formula for the oscillations of a mechanical system in which the constraints and the potential are variable very slowly with time.
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