  Autoresonance is a phase locking phenomenon occurring in nonlinear
oscislatory system, which is forced by oscillating perturbation. Many physical
applicatcons of the autoresonance are known in nonlenear physics. The essence
of the phenomecon is that the nonlinear oscillator selfadjusts to the varying
external conditions so that it remains in resonance with the orivvr for a long
time. This long time resonance leads to a strong increase in the response
amplitude under weak drivinc perturbation. An analytic treatment of a simple
mathematical model is done here by means of asymptotic analysis using a small
driving parameter. The main result is finding threshold for entering the
autoresonance.
