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

For the differential equation:

[tex] x'' + cx' + kx = F_{0}cos(\omage t) [/tex]

verify that the forced response takes the form, [tex] x_{f}(t) = Ccos(\omega t - \delta) [/tex]

2. Relevant equations

[tex] C = \frac { F_{0} } {\sqrt {(k- \omega ^{2})^{2} + c^{2} \omega ^{2} } }[/tex]

[tex] tan(\delta) = \frac {c \omega} {k - \omega ^ {2} }[/tex]

3. The attempt at a solution

I have tried to substitute [tex] x_{f}(t) = Ccos(\omega t - \delta) [/tex]

into the equation then equate the two sides but i am lost on how i would get the [tex] cos(\omega t - \delta) [/tex] into [tex] cos(\omega t ) [/tex]. The only way i saw that can do this is the trig identity [tex] cos(\omega t - \delta) = cos(\omega t)cos(-\delta) + sin(\omega t )sin(\delta)) [/tex] but doing this seems only to over complicate the problem.

Is the "forced response" just to solution to the system or is it something more specific than that?

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# Homework Help: Verify forced response.

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