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Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on interval: 0

Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on interval: 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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List To Apply 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?) b) Then decide that Fourier series has only sine terms. (-1)"+1 n c) If F(t) = 4 and x(t) = bnsin nt, find x"(t) substitute into original equation and find bn sin(nx)
Transcribed Image Text:List To Apply 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?) b) Then decide that Fourier series has only sine terms. (-1)"+1 n c) If F(t) = 4 and x(t) = bnsin nt, find x"(t) substitute into original equation and find bn sin(nx)
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