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Consider the periodic function f(t) with fundamental interval -7

Consider the periodic function f(t) with fundamental interval -7

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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Q1
Consider the periodic function f(t) with fundamental interval –7 <t < that is defined by -t - T for -T <t< 0, f(t) : for 0 <t < T, f(t+ 2π) = f(t). (a) Sketch the graph of the function f for -3T <t< 3n, and hence state whether the function is even, odd, or neither even nor odd. (b) Calculate the Fourier series for f(t) and hence show that the first few terms are 3 2 F(t) - cos(t) – cos(3t) 9T -IT 4 1 1 - sin(t) + sin(2t) - sin(3t). 2 3
Transcribed Image Text:Consider the periodic function f(t) with fundamental interval –7 <t < that is defined by -t - T for -T <t< 0, f(t) : for 0 <t < T, f(t+ 2π) = f(t). (a) Sketch the graph of the function f for -3T <t< 3n, and hence state whether the function is even, odd, or neither even nor odd. (b) Calculate the Fourier series for f(t) and hence show that the first few terms are 3 2 F(t) - cos(t) – cos(3t) 9T -IT 4 1 1 - sin(t) + sin(2t) - sin(3t). 2 3
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