关键词: singular perturbation, multiple scale, nonlinear oscillators, asymptotic analysis

Abstract: An initially periodic motion is gradually raised out of the potential well by the effect of negative damping. The elapsed time when the motion ceases to be periodic is obtained by multiple variable expansions. An example of a strictly nonlinear system shows the result has a good approximation and is easy to calculate.

Key words: singular perturbation, multiple scale, nonlinear oscillators, asymptotic analysis