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2. Given the periodic function over the period [-π/2, π/2] f(x) = x |x| a. Plot f(x) on the interval [-л, π] b. Is the function even or odd? c. Determine ao, an, bn. d. Setup the Fourier Series Expansion of f(x)

2. Given the periodic function over the period [-π/2, π/2] f(x) = x |x| a. Plot f(x) on the interval [-л, π] b. Is the function even or odd? c. Determine ao, an, bn. d. Setup the Fourier Series Expansion of f(x)

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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1. Given the plot of the function f(t) in one period, determine completely the Euler coefficients and write its Fourier series expansion. 3 f(t) -3 13 -3 2 -1 0, C₂ t 10 t 2. Given the periodic function over the period [-π/2, π/2] f(x) = x |x| a. Plot f(x) on the interval [-, π] b. Is the function even or odd? c. Determine ao, an, bn. d. Setup the Fourier Series Expansion of f(x) 2 3 3. Given the periodic function below defined over a period, determine completely the Euler coefficients and write its Fourier series expansion. f(x) = -c<x<0 0<x<c 4. Find the Fourier cosine expansion of f(x)= x²(3L-2x) on [0,L]. 5. Solve the one-dimensional wave equation for a string of length 10 units, fixed on both ends, with a = 3, if the string is initially at rest and with an initial displacement of y(x,0) = x for 0<x< 10.
Transcribed Image Text:1. Given the plot of the function f(t) in one period, determine completely the Euler coefficients and write its Fourier series expansion. 3 f(t) -3 13 -3 2 -1 0, C₂ t 10 t 2. Given the periodic function over the period [-π/2, π/2] f(x) = x |x| a. Plot f(x) on the interval [-, π] b. Is the function even or odd? c. Determine ao, an, bn. d. Setup the Fourier Series Expansion of f(x) 2 3 3. Given the periodic function below defined over a period, determine completely the Euler coefficients and write its Fourier series expansion. f(x) = -c<x<0 0<x<c 4. Find the Fourier cosine expansion of f(x)= x²(3L-2x) on [0,L]. 5. Solve the one-dimensional wave equation for a string of length 10 units, fixed on both ends, with a = 3, if the string is initially at rest and with an initial displacement of y(x,0) = x for 0<x< 10.
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