nonlinear positional friction

The variations of a system with one degree of freedom in the presence of nonlinear positional friction were considered. The restoring force of the oscillator's elasticity is described by the power function. A nonlinear solution of the Cauchy problem for the case of a power nonlinearity of positional friction were constructed. It is expressed through known periodic Ateb functions, which in recent years have become widespread in the theory of oscillations thanks to the efforts of the Lviv School of Mathematics and Mechanics.