Problem 6. A Fourier series for f(x) = x, where 0

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 57E
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Solve all parts of both problems 6 and 7
List To Apply
Problem 6. A Fourier series for f(x) = x, where 0<x< 2 is:
4
f(x) = Σ – сos nπ sin
πη
Fourier+Series
differentiate term by term and explain if the series
Converge to f'(x).
nπX
2
Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t)
Where F(t) = 2t on interval: 0<t<π.
a) First show F(t) = 2t is odd function and period is 2π (Why?)
(-1)2+1
b) Then decide that Fourier series has only sine terms.
n
- sin(nx)
c) If F(t) = 4
and x(t)=b,sin nt, find x"(t) substitute into original equation and find bn
F
Transcribed Image Text:List To Apply Problem 6. A Fourier series for f(x) = x, where 0<x< 2 is: 4 f(x) = Σ – сos nπ sin πη Fourier+Series differentiate term by term and explain if the series Converge to f'(x). nπX 2 Problem 7. Find a periodic Solution as a Fourier series to x" + 3x = F(t) Where F(t) = 2t on interval: 0<t<π. a) First show F(t) = 2t is odd function and period is 2π (Why?) (-1)2+1 b) Then decide that Fourier series has only sine terms. n - sin(nx) c) If F(t) = 4 and x(t)=b,sin nt, find x"(t) substitute into original equation and find bn F
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