Осцилятор Дуффинга. Астахов В.В - 29 стр.

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γ
0
: ¨x
0
+ x
0
= 0,
γ
1
: 2ω
1
¨x
0
+ ¨x
1
+ x
1
+ x
3
0
= 0,
¨x
1
+ x
1
= 2ω
1
¨x
0
x
3
0
.
x
0
= a cos(τ + φ)
= a cos(ωt + φ).
¨x
1
+ x
1
= 2ω
1
a cos(τ + φ) a
3
cos
3
(τ + φ),
¨x
1
+ x
1
= 2ω
1
a cos(τ + φ) a
3
[
3
4
cos(τ + φ) +
1
4
cos 3(τ + φ)].
x
1
(τ) cos(τ+
φ)
τ
x
1
(τ)
2ω
1
a
3a
3
4
= 0,
ω
1
=
3a
2
8
.
¨x
1
+ x
1
=
a
3
4
cos 3(τ + φ).
x
1
= C cos 3(τ + φ).