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A periodic function f(t) has a Fourier series (−1)" + 1 n² F(t) = 2 + ∞ ∞ cos(nat) + n=1 (²) sin(nnt). n=1 Select the option that gives first few terms of the Fourier series up to and including terms involving 3πt. Select one: 2 + cos(nt) + -cos(3mt) + sin(at) + sin(2πt) + =sin(3at) 1 1 2+ = cos(2πt) + sin(nt) + sin(2at) + sin(3mt) 9 2 + 2 cos(nt) + ²-cos(3πt) + sin(nt) + =sin(2nt) + — sin(3πt) 2+2 cos(tt)+2 cos(37t)+sin(t) +sin(27t)+sin(3t) 2+2 cos(27t)+sin(tt)+sin(27t)+sin(37t)

A periodic function f(t) has a Fourier series (−1)" + 1 n² F(t) = 2 + ∞ ∞ cos(nat) + n=1 (²) sin(nnt). n=1 Select the option that gives first few terms of the Fourier series up to and including terms involving 3πt. Select one: 2 + cos(nt) + -cos(3mt) + sin(at) + sin(2πt) + =sin(3at) 1 1 2+ = cos(2πt) + sin(nt) + sin(2at) + sin(3mt) 9 2 + 2 cos(nt) + ²-cos(3πt) + sin(nt) + =sin(2nt) + — sin(3πt) 2+2 cos(tt)+2 cos(37t)+sin(t) +sin(27t)+sin(3t) 2+2 cos(27t)+sin(tt)+sin(27t)+sin(37t)

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 periodic function f(t) has a Fourier series + ² Σ -1)” (-(-1)/² + 1) cos(nπt) + n=1 Select the option that gives first few terms of the Fourier series up to and including terms involving 3πt. F(t) = 2 + Select one: 1 2 + cos(πt) + = cos(3πt) + sin(nt) + 4 2+ cos(nπt) + Σ (n−²) sin(nπt). Σ n=1 2 9 1 sin(2πt) + sin(3rt) 9 1 1 — cos(2πt) + sin(rt) + =sin(2πt) + sin(3rt) 1 1 cos(3nt) + sin(nt) + sin(2nt) + =sin(3rt) 4 2+2 2+2 cos(tt)+2 cos(37t)+sin(7t) +sin(27t) + sin(37t) 2+2 cos(27t)+sin(tt) +sin(27t)+sin(37t)
Transcribed Image Text:A periodic function f(t) has a Fourier series + ² Σ -1)” (-(-1)/² + 1) cos(nπt) + n=1 Select the option that gives first few terms of the Fourier series up to and including terms involving 3πt. F(t) = 2 + Select one: 1 2 + cos(πt) + = cos(3πt) + sin(nt) + 4 2+ cos(nπt) + Σ (n−²) sin(nπt). Σ n=1 2 9 1 sin(2πt) + sin(3rt) 9 1 1 — cos(2πt) + sin(rt) + =sin(2πt) + sin(3rt) 1 1 cos(3nt) + sin(nt) + sin(2nt) + =sin(3rt) 4 2+2 2+2 cos(tt)+2 cos(37t)+sin(7t) +sin(27t) + sin(37t) 2+2 cos(27t)+sin(tt) +sin(27t)+sin(37t)
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