solve for the particular solution of the damped harmonic oscillator driven by the damped harmonic force(adsbygoogle = window.adsbygoogle || []).push({});

[tex] F(t) = F_0e^{-\alpha t)cos(\omega t)[/tex]

(Hint: [tex]e^{-\alpha t} cos(\omega t) = Re[e^{-\alpha t + i \omega t}] = Re[e^{B t}][/tex] where [tex]B = -\alpha + i \omega[/tex]. Find the solution in the form [tex]x(t) = De^{B t - i \phi} [/tex], i don't have much diff e q the only thing i think of doing is the following..

[tex]x'' + 2 \gamma x' + \omega^2 x = 0 [/tex]

[tex] c^2 + 2 \gamma c + \omega^2 = 0 [/tex]

[tex] x(t) = C_1 e^{-(\sqrt{\gamma^2 - \omega^2}+\gamma)t} + C_2 e^{(\sqrt{\gamma^2 -\omega^2}-\gamma) t}[/tex]

no idea where to go from here... any help would be awesome

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# Homework Help: Particular differnetial solution

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