The article analyzes the influence of the non-linear terms of the restoring force at large deviations from the equilibrium position of an oscillating body (non-linear oscillator). Particularly, it is demonstrated, in an accessible way,that the oscillations of the anharmonic oscillator drastically differ from thoseof a harmonic one. The main reason lies in the fact the oscillator frequency ofthe nonlinear oscillator, at large deviations, begins to depend on the amplitudeof the oscillations.