Lecture 23: Two-timing

The simplest version of the method of multiple scales is known as two-timing. It exploits the separation between a fast time scale (on which oscillations or some other kind of dynamics typically occur) and a much slower time scale (on which the amplitude of those oscillations gradually change or other aspects of the dynamics gradually evolve). Prof. Strogatz illustrates the method by applying it to two classic problems about oscillators. The first problem -- the motion of a weakly damped linear oscillator -- is exactly solvable, and serves as test case to calibrate the two-timing method. The second problem involves the van der Pol oscillator, one of the most famous systems in nonlinear dynamics. Two-timing yields very accurate predictions of the oscillator's long-term amplitude, as well as the transient approach to its limit cycle. Finally, a high point of the lecture is an unexpected visit by Prof. Strogatz's dog, Murray, at around 15:45.