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# Fourier Series Help! watch

1. Hi all

I've got a question on Fourier series, I know the answer i should be getting, however i'm getting the opposite sign. I've checked my work and just cant see where i have gone wrong, please help. Ill put my working below.
If someone could inform me why im getting 12/(pi)(n) instead of -12/(pi)(n), i would be very grateful

Attached Images

2. (Original post by Ramjam)
Hi all

I've got a question on Fourier series, I know the answer i should be getting, however i'm getting the opposite sign. I've checked my work and just cant see where i have gone wrong, please help. Ill put my working below.
If someone could inform me why im getting 12/(pi)(n) instead of -12/(pi)(n), i would be very grateful

I'm a little puzzled as to where you got your expression for . . .
Should it not be ?
With this expression the result you want follows.

Edit: Also what is here? You've written it in some places, and not others. . .
An image of the question itself might be useful.
3. (Original post by joostan)
I'm a little puzzled as to where you got your expression for . . .
Should it not be ?
With this expression the result you want follows.

Edit: Also what is here? You've written it in some places, and not others. . .
An image of the question itself might be useful.
It came from 'Modern Engineering Mathematics by Glyn James', it states that i can use that formula specifically for odd function. However I will work through using the original formula for bn and see what answer I achieve.

The question is on the working, in black pen, it is to find the fourier series of f (t) = 3 (-pi < t < 0) -3 (0 < t < pi
4. (Original post by Ramjam)
It came from 'Modern Engineering Mathematics by Glyn James', it states that i can use that formula specifically for odd function. However I will work through using the original formula for bn and see what answer I achieve.

The question is on the working, in black pen, it is to find the fourier series of f (t) = 3 (-pi < t < 0) -3 (0 < t < pi
I can't say I've seen that formula before, so I can't comment as to what's gone on there.
All I can see is that for an odd function on one can rewrite: .

Yeah, I figured that was the question, but then I don't see what has to do with anything.
5. (Original post by joostan)
I can't say I've seen that formula before, so I can't comment as to what's gone on there.
All I can see is that for an odd function on one can rewrite: .

Yeah, I figured that was the question, but then I don't see what has to do with anything.
The issue is just me making mistakes again (sorry)

I've reworked the question and reached a point in which i'm unsure on where to go from here. Whats do i have to do next? The point at which you assign odd and even values of n, although sounds simple always confuses me.
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6. (Original post by Ramjam)
The issue is just me making mistakes again (sorry)

I've reworked the question and reached a point in which i'm unsure on where to go from here. Whats do i have to do next? The point at which you assign odd and even values of n, although sounds simple always confuses me.
There seems to be a mistake prior to that: changes sign in the interval, so you'll want to write:
.
7. (Original post by joostan)
There seems to be a mistake prior to that: changes sign in the interval, so you'll want to write:
.
Whats happens after that? do you integrate between limits separately for both of those?
8. (Original post by Ramjam)
Whats happens after that? do you integrate between limits separately for both of those?
You could do that, or you could send in either integral to obtain a single integral, it doesn't really matter.
9. (Original post by joostan)
You could do that, or you could send in either integral to obtain a single integral, it doesn't really matter.
Well i'm getting no where quick, i just cant seem to get my head around this question, i must be making mistakes somewhere as it keeps going completly wrong
10. (Original post by Ramjam)
Well i'm getting no where quick, i just cant seem to get my head around this question, i must be making mistakes somewhere as it keeps going completly wrong
Spoiler:
Show

These integrals are then simple to evaluate.
11. (Original post by joostan)
Spoiler:
Show

These integrals are then simple to evaluate.
from here would you integrate them to get it in terms of cos?
12. (Original post by Ramjam)
from here would you integrate them to get it in terms of cos?
Well I actually used the fact that is odd to write.
But you could just as well integrate now.
13. Hint: (Since the integrand is an even function.)

14. (Original post by poorform)
Hint: (Since the integrand is an even function.)

You dropped a minus in your expression for .
15. (Original post by joostan)
You dropped a minus in your expression for .
Will update now thanks!

I (wrongly) assumed that f(t) was positive for positive t and negative for negative t.

Since I did a very similar question the other day that was defined that way haaaaa.

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