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A function with a period 2L is This function f(x) presents in Fourier Series as 00 5 n=1 (a) (b) (c) (d) f(x) = a₁ + where the Fourier coefficients are given by an bn f(x) = { A₁ 1 = = -L 1 L 10 -L an cos ao -B≤x≤0 0

A function with a period 2L is This function f(x) presents in Fourier Series as 00 5 n=1 (a) (b) (c) (d) f(x) = a₁ + where the Fourier coefficients are given by an bn f(x) = { A₁ 1 = = -L 1 L 10 -L an cos ao -B≤x≤0 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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A=4,B=2

A=4,B=2

 

3. A function with a period 2L is f(x) = { A A, 0, This function f(x) presents in Fourier Series as (a) (b) (c) (d) f(x) = ao + (e) ∞ Σ n=1 where the Fourier coefficients are given by 1 L - 2/7 [+ f(x) dx 2L an = do -B<x<0 0 < x <B ηπχ an cos + L 1 bn = [ f(x) sin(! -L 00 Σbn n=1 nπX L L 1 = f(x) cos(17) dx (n = 1,2,3,...) L -L sin ηπχ L dx (n = 1,2,3,...) Write the function according to the input variables of A and B. Sketch one period of the function for part (a). Determine the period of 2L from part (b). Determine the Fourier coefficients of this function f(x). Write down the corresponding Fourier series.
Transcribed Image Text:3. A function with a period 2L is f(x) = { A A, 0, This function f(x) presents in Fourier Series as (a) (b) (c) (d) f(x) = ao + (e) ∞ Σ n=1 where the Fourier coefficients are given by 1 L - 2/7 [+ f(x) dx 2L an = do -B<x<0 0 < x <B ηπχ an cos + L 1 bn = [ f(x) sin(! -L 00 Σbn n=1 nπX L L 1 = f(x) cos(17) dx (n = 1,2,3,...) L -L sin ηπχ L dx (n = 1,2,3,...) Write the function according to the input variables of A and B. Sketch one period of the function for part (a). Determine the period of 2L from part (b). Determine the Fourier coefficients of this function f(x). Write down the corresponding Fourier series.
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