Many contributors to theoretical syntax and phonology, e.g. Goldsmith, Uriagereka, Vergnaud, Idsardi, Smolensky, and Prince, have used dynamical systems analysis to make sense of some fundamental computational properties of natural language. Yet, dynamical systems analysis does not usually form part of the linguistics curriculum. In this tutorial, dynamical systems analysis will be introduced from scratch, then two case studies will be summarized: 1) Uriagereka's work on phase periodicity and frustration; 2) Goldsmith, Prince and Idsardi's work on syllabification and metricity; The tutorial will concentrate on the fundamental ideas, and why dynamical systems analysis has seduced many linguists in the past.