Finding the Fourier Series of a Cosine Function.

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Homework Help Overview

The problem involves finding the Fourier series of the function f(x) = Acos(∏x/L). Participants discuss the properties of the function, including its periodicity and whether it is even, as well as the appropriate Fourier series representation to use.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Some participants question the original poster's assumption that the function is even and periodic over the specified range. Others suggest that the Fourier series should account for the function's period of 2L instead of 2π.

Discussion Status

There is an ongoing exploration of the correct approach to the Fourier series, with participants providing insights into the definitions and relationships between the variables involved. Some guidance has been offered regarding the use of trigonometric identities and the importance of clarifying the function's periodicity.

Contextual Notes

Participants note that the original poster is working from ambiguous study materials and lacks a textbook, which may contribute to confusion regarding the definitions and relationships of the variables L and D in the context of Fourier series.

  • #31
Uart,
The question is posted in bold a few posts back and that is exactly how it appears on the piece of paper I have So yeah there's as lot of assuming it seems
 
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  • #32
I don't think there is much left to be said about this problem. Yes, the statement of the problem leaves lots go be desired. However, given the way it was stated, the natural assumption is that L is a half period, which is the usual notation. And the point of the problem is for the student to learn a couple of things.

1. The function itself is its own finite Fourier Series.
2. That if you calculate the Fourier Coefficients you need to be careful about using identities (in this case because of the situation when n=1).
 
  • #33
Agreed. I'd just like to thank you all for your input though, much appreciated! (:
 
  • #34
ProPatto16 said:
Uart,
The question is posted in bold a few posts back and that is exactly how it appears on the piece of paper I have So yeah there's as lot of assuming it seems

Ok I see it now, thanks.
Given the function f(x) = Acos(∏x/L), determine its Fourier series.

there is nothing else, no domain specified or anything.

That's just a poorly written question. Take the period as whatever you want in that case, using 2L is definitely the easiest. :smile:
 

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