4. Find the Fourier cosine expansion of f(x) = x²(3L-2x) on [0,L].
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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Upp. 4 and 5 solve
![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
0,
C,
12
1
t
10
2. Given the periodic function over the period [-π/2, π/2]
f(x) = x |x|
t
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. 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].
3
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%2F77804015-4699-41fc-b2fd-c6a28b984858%2F8bfaa8b6-ac47-4afd-b804-8b224e56e48a%2Fpc38tse_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
13
-3
0,
C,
12
1
t
10
2. Given the periodic function over the period [-π/2, π/2]
f(x) = x |x|
t
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. 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].
3
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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