Given the periodic function over the period [-1/2, 1/2] f(x) = x |x| a. Plot f(x) on the interval [-n, a] b. Is the function even or odd? c. Determine ao. an, bn. d. Setup the Fourier Series Expansion of f(x)
Given the periodic function over the period [-1/2, 1/2] f(x) = x |x| a. Plot f(x) on the interval [-n, a] b. Is the function even or odd? c. Determine ao. an, bn. d. Setup the Fourier Series Expansion of f(x)
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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Qno2 solve all parts okkk
![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
3
-3
12
1
+
1
2. Given the periodic function over the period [-/2, n/2]
f(x) = x x
a. Plot f(x) on the interval [-n, ]
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) = ¹0,
-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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ab0fb29-2c34-45df-b1d3-efd8add8675a%2F5d422806-30c8-47c2-93d7-5b8dfc1e8697%2Fc2k6hgk_processed.jpeg&w=3840&q=75)
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
3
-3
12
1
+
1
2. Given the periodic function over the period [-/2, n/2]
f(x) = x x
a. Plot f(x) on the interval [-n, ]
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) = ¹0,
-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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