
303Nonlinear Oscillations
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the time axis. For example, if the driving force is sinusoidal with angular frequency F = F
0
cosωt,
then the period T of the driving force is given by T = 2π/ω. If we want n points per cycle of the driv-
ing force, we can set the step size h with the formula h = 2π/(nω).
The power spectrum is computed using Fourier analysis to display the frequency composition of
time variation of the dynamic variables.
Example 9.7
Find the Poincare map of period 2π for the solution of the following equation:
64 16 65 64
xxx t++= cos
(9.104)
which starts from (0,0) at time t = 0.
Solution:
The general solutio ...