Sample Exam Fourier Series & reverse engineering the question

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Homework Help Overview

The discussion revolves around a sample exam question related to Fourier series in the context of engineering mathematics. Participants are exploring the properties of a Fourier series that contains only sine terms, questioning its implications regarding the function's oddness and period calculation. Additionally, there is a query about constructing a "deleted diagram" from the Fourier series, which has not been covered in their coursework.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the nature of the Fourier series, particularly the significance of having only sine terms and its relation to odd functions. There are inquiries about the calculation of the period and the feasibility of drawing a diagram related to the series. One participant suggests a potential interpretation of the function involved, while another raises a question about the series resembling a reverse square wave.

Discussion Status

The discussion is ongoing, with participants sharing their thoughts and interpretations. Some guidance has been offered regarding the properties of the Fourier series, but there is no clear consensus on the specific function or the diagram in question. The exploration of multiple interpretations is evident.

Contextual Notes

Participants note that they have not yet covered certain aspects of the topic, such as the "deleted diagram," which adds a layer of complexity to their inquiries. There is also mention of specific coefficients and functions that may or may not align with the Fourier series being discussed.

pat666
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Homework Statement


Hey,
This is a question from a sample exam we are given for our engineering maths exam. Firstly given that the Fourier series contains only "sin(x)" doesn't this mean that it is an "odd" function? Can the period be calculated from the given function easily?

Secondly is it possible to draw the "deleted diagram" from the given Fourier series (we haven't learn't this but it should be shouldn't it)? If it is can someone please draw it and then help me do question iii.

Thankyou

PS, if anyone is willing to draw it or get matlab/mathematica to, can you post it and then I will attempt the question and repost.

Homework Equations





The Attempt at a Solution

 

Attachments

  • sample exam.png
    sample exam.png
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pat666 said:

Homework Statement


Hey,
This is a question from a sample exam we are given for our engineering maths exam. Firstly given that the Fourier series contains only "sin(x)" doesn't this mean that it is an "odd" function? Can the period be calculated from the given function easily?

Secondly is it possible to draw the "deleted diagram" from the given Fourier series (we haven't learn't this but it should be shouldn't it)? If it is can someone please draw it and then help me do question iii.

Thankyou

PS, if anyone is willing to draw it or get matlab/mathematica to, can you post it and then I will attempt the question and repost.

Homework Equations


The Attempt at a Solution

If your Fourier expansion has only sine terms, it is indeed an odd function, so the An coefficient is 0. I suppose by "max and min of 1 and -1" they mean t\in[-1,1]

r(t) could be the unit step function scaled to -4, when 0<t<1. That would give you the Bn coefficient you've got, but it could've been something else too I think.

Edit: Noticed there's no -4 as a 0th term in the series, so I'm probably wrong. Looks like you need a function that integrated from -1 to 1 gives you zero, but integrated while multiplied by sin(n*t)/pi gives you -4/pi*n
 
is this a reverse square wave?
the series looks similar to this?
 

Attachments

  • Screen shot 2011-05-30 at 11.26.50 PM.png
    Screen shot 2011-05-30 at 11.26.50 PM.png
    7.8 KB · Views: 577
I'm not sure, I was hoping PF could help me out.
 

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