About zeros of some oscillations with dynamic friction

MARCOV Nicolae
2014 INCAS Bulletin  
Consider a second order differential non-linear equation having free boundary value conditions. Let be a solution having infinity of unknown zeros. The integral of energy gives the implicit correlation between the successive modules of the extreme values of oscillation. The method of successive approximations transforms this correlation into an algorithmic correlation. The decreasing sequence of the modules or local amplitudes converges to zero. For the local amplitude of oscillation inside the
more » ... illation inside the interval of two successive zeros, the length of the interval is a sum of two improper integrals. In order to obtain the values of these integrals, it is necessary to use series expansions. If the coefficient of dynamic friction is small and the amplitude reached a low enough value, then the polynomial functions are given for the numerical calculus of distances between zeros of the oscillation.
doi:10.13111/2066-8201.2014.6.s1.10 fatcat:tdxcseqi3vedlb7vm3qhuk2apy