Answered: f(t) = {t+2, –2

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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Question

Calculate the expansion and the corresponding Fourier series in trigonometric form
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Expert Solution

Step 1

Given function,

$f (t) = {t + 2, - 2 \leq t < 0$

The Fourier series representation of $f (t)$ in the interval $(- L, L)$ is given by

$f (t) = \frac{a_{0}}{2} + \sum_{n = 1}^{\infty} [a_{n} \cos (\frac{n πt}{L}) + b_{n} \sin (\frac{n πt}{L})] where a_{0} = \frac{1}{L} \int_{- L}^{L} f (t) d t a_{n} = \frac{1}{L} \int_{- L}^{L} f (t) \cos (\frac{n πt}{L}) d t b_{n} = \frac{1}{L} \int_{- L}^{L} f (t) \sin (\frac{n πt}{L}) d t$

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