
298 Classical Mechanics
© 2010 Taylor & Francis Group, LLC
the solution x
1
+ x
2
is put into the right-hand side of Equation 9.88. This iterative process is repeated
as often as desired. As an illustrative example, consider the Dufng’s equation, but solve it only as
far as the second approximation.
Example 9.6: Duffing’s Equation
If we replace F(x) in Equation 9.88 by −εx
3
, the resulting equation is known as the Duffing equation:
mx kx xf t
3
cos (9.90)
or
xx
x
f
t=− ++ω
ε
ω
0
23
cos . (9.91)
Considering that the nonlinear term is small and can be neglected, we obtain
xx
f
10
2
1
+=
cos . (9.92)
This is a simple harmonic oscillator driven by an externa ...