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Figure 1 shows a periodic function, f(x), with period of 2. f(x) wimm -π O π (a) State if the function f(x) has odd or even symmetry. 2 A = ao (b) Show that the Fourier coefficients of f(x) are given by: TU -a Figure 1 a₁ = 2A 1+(-1)" 1-n² T f(x)= Asinx if 0

Figure 1 shows a periodic function, f(x), with period of 2. f(x) wimm -π O π (a) State if the function f(x) has odd or even symmetry. 2 A = ao (b) Show that the Fourier coefficients of f(x) are given by: TU -a Figure 1 a₁ = 2A 1+(-1)" 1-n² T f(x)= Asinx if 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Figure 1 shows a periodic function, f(x), with period of 2. f(x) wimm -π O π ao = (a) State if the function f(x) has odd or even symmetry. 2 A (b) Show that the Fourier coefficients of f(x) are given by: TC Figure 1 a₁ = 2A 1+(-1)" 1-n² T f(x)= Asinx if 0<x<a - Asinx if -≤x≤0 f(x)= A is a constant. b₁ = 0 Hint: You will find the result in question 1(b) useful to find an. Also, remember that ƒ ƒodt (x)dx = 0, ƒ ƒeven (x) dx = 2 feven (x) dx -a -a 0 - 24_44 ( cos(2x) + = cos(4x) + 2A TU TU 15 (c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x) is given by: 1 +cos -cos(6x) + ... 35
Transcribed Image Text:Figure 1 shows a periodic function, f(x), with period of 2. f(x) wimm -π O π ao = (a) State if the function f(x) has odd or even symmetry. 2 A (b) Show that the Fourier coefficients of f(x) are given by: TC Figure 1 a₁ = 2A 1+(-1)" 1-n² T f(x)= Asinx if 0<x<a - Asinx if -≤x≤0 f(x)= A is a constant. b₁ = 0 Hint: You will find the result in question 1(b) useful to find an. Also, remember that ƒ ƒodt (x)dx = 0, ƒ ƒeven (x) dx = 2 feven (x) dx -a -a 0 - 24_44 ( cos(2x) + = cos(4x) + 2A TU TU 15 (c) By evaluating the first six Fourier coefficients show that the Fourier series of f(x) is given by: 1 +cos -cos(6x) + ... 35
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