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Problem 6. A Fourier series for f(x) = x, where 0

Problem 6. A Fourier series for f(x) = x, where 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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Solve all parts of both problems 6 and 7
List To Apply Problem 6. A Fourier series for f(x) = x, where 0<x< 2 is: 4 f(x) = Σ – сos nπ sin πη Fourier+Series differentiate term by term and explain if the series Converge to f'(x). nπX 2 Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on interval: 0<t<π. a) First show F(t) = 2t is odd function and period is 2π (Why?) (-1)2+1 b) Then decide that Fourier series has only sine terms. n - sin(nx) c) If F(t) = 4 and x(t)=b,sin nt, find x"(t) substitute into original equation and find bn F
Transcribed Image Text:List To Apply Problem 6. A Fourier series for f(x) = x, where 0<x< 2 is: 4 f(x) = Σ – сos nπ sin πη Fourier+Series differentiate term by term and explain if the series Converge to f'(x). nπX 2 Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on interval: 0<t<π. a) First show F(t) = 2t is odd function and period is 2π (Why?) (-1)2+1 b) Then decide that Fourier series has only sine terms. n - sin(nx) c) If F(t) = 4 and x(t)=b,sin nt, find x"(t) substitute into original equation and find bn F
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