Unsymmetrical oscillations A non-linear oscillator satisfies the equation
x·· + x + ?x2 = 0,
where ? is a small parameter. Explain why the oscillations are unsymmetrical about x = 0 in this problem.
Use Linstedt's method to obtain a two-term approximation to x(t) for the oscillation in which the maximum value of x is unity. Deduce a two-term approximation to the minimum value achieved by x(t) in this oscillation.