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http://dl.dropbox.com/u/33103477/Linear%20oscilator.png [Broken]

I am having trouble understand the question, what I have done its solve the equation using the substitution [tex]x=e^{rx}[/tex]

Then, I have the solution given by:

[tex] x(t)=c_1 e^{t(\sqrt{\gamma^2 - \omega^2 })} + c_2e^{-t(\sqrt{\gamma^2 - \omega^2)}} [/tex]

So at x(0)=0,

[tex] c_1 + c_2 = 0[/tex]

and, x'(0)=v

[tex] v=c_2(\sqrt{\gamma^2 - \omega^2} - \omega) + c_1(\sqrt{\gamma^2 - \omega^2}+\omega) [/tex]

Not quite sure how to proceed as if \omega is greater than \gamma I get imaginary values and the opposite gives real, but what does that mean ?

I am having trouble understand the question, what I have done its solve the equation using the substitution [tex]x=e^{rx}[/tex]

Then, I have the solution given by:

[tex] x(t)=c_1 e^{t(\sqrt{\gamma^2 - \omega^2 })} + c_2e^{-t(\sqrt{\gamma^2 - \omega^2)}} [/tex]

So at x(0)=0,

[tex] c_1 + c_2 = 0[/tex]

and, x'(0)=v

[tex] v=c_2(\sqrt{\gamma^2 - \omega^2} - \omega) + c_1(\sqrt{\gamma^2 - \omega^2}+\omega) [/tex]

Not quite sure how to proceed as if \omega is greater than \gamma I get imaginary values and the opposite gives real, but what does that mean ?

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