(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img51.imageshack.us/img51/853/39983853.jpg [Broken]

2. The attempt at a solution

Q3.1

I get the general solution as

[tex]x(t) = Ae^{3t}+Be^{-t} + cost - 2sint[/tex] .

Q3.2

Letting

[tex]y=\dot{x}[/tex]

and using the general solution, we get

[tex]y=3Ae^{3t}-Be^{-t}-sint-2cost[/tex] .

Therefore the solution in the form they ask for is

[tex](Ae^{3t}+Be^{-t} + cost - 2sint, 3Ae^{3t}-Be^{-t}-sint-2cost, t)[/tex] .

Or am I misunderstanding?

Q3.3

[tex]x_{0}=x(0)=A+b-1 , y_{0}=y(0)=3A-B-2[/tex] .

Solving these simultaneously gives

[tex]A=0.25(x_{0}+y_{0}+1) , B=0.25(3x_{0}-y_{0}-5)[/tex]

so the PoincarĂ© mapping is

[tex](0.25(x_{0}+y_{0}+1)e^{3t}+0.25(3x_{0}-y_{0}-5)e^{-t}+cost-2sint, 0.75(x_{0}+y_{0}+1)e^{3t} - 0.25(3x_{0}-y_{0}-5)e^{-t}-sint - 2cost, t)[/tex]

Is that correct so far?

To find the fixed points, do I let x(2pi)=x(0), y(2pi)=y(0) and solve for x(0) and y(0)? I tried this but I get something ridiculously complicated, so I'm worried i'm not understanding the question correctly at all...

Please help! :-( Thanks.

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# Homework Help: Nonlinear Oscillations

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