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**Diff Eq--Particular solution with fourier cosine/sine series**

## Homework Statement

Find the particular solution x

_{p}(t) of equation [tex]m\frac{d^{2}x}{dt^{2}}+kx=f(t)[/tex] when [tex]m=\frac{1}{4}[/tex] , k=12, f(t) is given. Assume that when f(t) is extended to the negative t-axis in a periodic manner, the resulting function is even.

## The Attempt at a Solution

So, What does it mean to extend f(t) to the negative t-axis in a periodic manner? And what does it mean when an example in the book says a 2p-periodic extension?

And how do I use [tex]f(t+2\pi)=f(t)[/tex]

Thanks for looking!