Fourier series understanding problem

[JI567]

Homework Statement

So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

Homework Equations

No relevant equation needed just don't understand which values of x to take.

The Attempt at a Solution

I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?! Please help...

 

[Chestermiller]

Homework Statement

So the question is how does

4/π*(sin(πx))+4/3π *(sin(3πx))+4/5π *(sin(5πx)) = 1

for values of 0<x<1

Homework Equations

No relevant equation needed just don't understand which values of x to take.

The Attempt at a Solution

I am not sure which value of x to start with, it could be anything 0.1 or 0.5, how do I know which x value to start with? I have taken 0.5 and ended up with 1.05 and then taken 0.9 and ended up with 1.15. How the hell does this equal to 1 for any x value?! Please help...

You're missing some terms in the series, starting with the sin(7πx) term. Was there a sequence of 3 dots ... in the equation you were given? The three dots indicate an infinite series.

Chet

 

[JI567]

Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity...but I still don't get it...can you explain how it equals 1...

 

[Chestermiller]

Yeah there were few other terms, the consecutive odd n's, I just didn't write it, sorry! and also yeah sequence of 3 dots so its infinity...but I still don't get it...can you explain how it equals 1...

Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet

 

[JI567]

Are you familiar with half-wave Fourier series? Or, can you expand the following function in a Fourier series:

y = -1 from x = -1 to x = 0

y = +1 from x = 0 to x = +1

Also, in terms of the series you have written, just try including more terms in the summation (say, up to 20) and see what you get when you evaluate the value at x = 0.5.

Chet

No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do Fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!

 

[Chestermiller]

No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do Fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!

I can't know what they ask you to do on your exams.

If the question is, "how well does the three term expression you wrote match y = 1 over the interval 0<x<1?", just plot a graph of the expression as a function of x. Evaluate x every 0.05 over the interval. You can use a spreadsheet to do this type of calculation easily. Then plot the graph. I think you will be surprised at how well it fits over the entire interval with only three terms.

Chet

 

[LCKurtz]

No I am not familiar with the half wave thingy. 20?! So in the exam when they ask me to do Fourier sine series and show the value they converge to. I will have to write down 20 terms and then add them up? omg!

More likely they are wanting you to know some of the theory about how a FS represents a function. Have you heard of the Dirichlet conditions? Do you know what the FS does when there is a jump discontinuity in the function? You don't have to literally add the series to know what the sum looks like.

 

[JI567]

Nope I don't...but you could always tell me...

 

[LCKurtz]

Nope I don't...but you could always tell me...

I could, but you can use Google as easily as I can, and you need to read and study a bit about it. One place that pops up on a google search is
http://www.physics.nus.edu.sg/~phylimhs/Fourier3.pdf

 

[JI567]

I could, but you can use Google as easily as I can, and you need to read and study a bit about it. One place that pops up on a google search is
http://www.physics.nus.edu.sg/~phylimhs/Fourier3.pdf

Can you explain page 15 please. How did ar just became 4/4 from 2/4? Because in general formula its always Ar = 2/L * etc. Secondly, how are the Ar from 2/4 equal to the one at 4/4. I don't get the integral range, like what they did in that problem