Find fe(), the Fourier series expansion of * € [-L, 0), * € [0, L], where k and L are positive constants.
Find fe(), the Fourier series expansion of * € [-L, 0), * € [0, L], where k and L are positive constants.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Find f(x), the Fourier series expansion of
0
* € [-L, 0),
=
{kº * € [0, 1],
where & and I are positive constants.
kL
kL
+)
2
22
²72 ((-1)^²+1 -1) cos(")
kl
fr(a) = k +
(k (-1)^ cos (¹7) +
4
kL
kL
=
- Σ( ²2 ((-1)² - 1) cos(-
(**) +
123T
R=1
kL
NTT
fr(2) = k + +Ë ( 22((-1)-1) cos(
4
22² 72
R=1
kL
= 1
kL
2
+ 2 (2)
(²72((−1)² + 1) cos (²) +
R=1
None of the options displayed.
kL
kL
MTX
fr(x) =
(-1)+¹ sin(
2
727T
fr(x) =
- ((-1) ² - 1) sin (7²)
:-)
127T
R=1
kL
fr(*) =
=
- (-1)²+¹ cos (7²)
12²772
L
R=1
+
R=1
00
iM8
((-1)+1-1) sin()
nπ
(-1)+1 sin(-
kL
727T20
+ (-1)+¹ sin(-
727T
L
kL
(-1) sin(7²))
123T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3d01a12a-1ab5-4b5b-8ac9-ffcff6df37dc%2F739c4c53-2706-4008-8c02-2c09e0785db5%2Frkuuelo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Find f(x), the Fourier series expansion of
0
* € [-L, 0),
=
{kº * € [0, 1],
where & and I are positive constants.
kL
kL
+)
2
22
²72 ((-1)^²+1 -1) cos(")
kl
fr(a) = k +
(k (-1)^ cos (¹7) +
4
kL
kL
=
- Σ( ²2 ((-1)² - 1) cos(-
(**) +
123T
R=1
kL
NTT
fr(2) = k + +Ë ( 22((-1)-1) cos(
4
22² 72
R=1
kL
= 1
kL
2
+ 2 (2)
(²72((−1)² + 1) cos (²) +
R=1
None of the options displayed.
kL
kL
MTX
fr(x) =
(-1)+¹ sin(
2
727T
fr(x) =
- ((-1) ² - 1) sin (7²)
:-)
127T
R=1
kL
fr(*) =
=
- (-1)²+¹ cos (7²)
12²772
L
R=1
+
R=1
00
iM8
((-1)+1-1) sin()
nπ
(-1)+1 sin(-
kL
727T20
+ (-1)+¹ sin(-
727T
L
kL
(-1) sin(7²))
123T
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