Determine the Fourier series expansion of the following periodic function: 2 = { ₁ + ²₁ 1, f(t) -5

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Determine the Fourier series expansion of the following periodic function:

A.
B.
C.
D.
Determine the Fourier series expansion of the following periodic function:
0 = { ₁ + ²₁
1,
9
y = =+
4
9
y = 4
+
5
9 5
y=+=
f(t)
00
9 5
y=+
7=1
00
n=1
CO
ΣΗ
n=1
00
Σ
[сos nπ - 1
n²π
n=1
[соs nπ - 1
nπ
[сos nπ
сos nπ- - 1
n²
n
COS
-5<t<0
0<t<5
COS
nπt
COS +
5
nπt
5
COS
nnt
5
nπt
5
сOS NÃ
n
+
сos ní
n²
-sin-
T
-sin
сos ní
сos ní - 1
n²π
nnt
5
-sin
nit
5
-sin
not
nπt
Transcribed Image Text:A. B. C. D. Determine the Fourier series expansion of the following periodic function: 0 = { ₁ + ²₁ 1, 9 y = =+ 4 9 y = 4 + 5 9 5 y=+= f(t) 00 9 5 y=+ 7=1 00 n=1 CO ΣΗ n=1 00 Σ [сos nπ - 1 n²π n=1 [соs nπ - 1 nπ [сos nπ сos nπ- - 1 n² n COS -5<t<0 0<t<5 COS nπt COS + 5 nπt 5 COS nnt 5 nπt 5 сOS NÃ n + сos ní n² -sin- T -sin сos ní сos ní - 1 n²π nnt 5 -sin nit 5 -sin not nπt
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