
283Nonlinear Oscillations
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9.3 FOURIER SERIES EXPANSIONS
The Fourier series method is quite versatile and applies in any situation where the motion is peri-
odic. As an example of application to nonlinear oscillations, we consider a free oscillation with
nonlinear restoring forces, where the potential energy is an arbitrary function of x, V = V(x). There is
no loss in generality by setting V(0) = 0 at the equilibrium position x = 0. We further limit ourselves
to a stable equilibrium where
V(x) > 0 for x ≠ 0 and dV(0)/dx = 0.
Then Taylor’s expansion of V(x), for small oscillations, at the equilibrium position ...