The following f(t) is a periodic function of period 27T, defined over the period 0≤t≤ 2. (2 cos² ()-1, when 0
The following f(t) is a periodic function of period 27T, defined over the period 0≤t≤ 2. (2 cos² ()-1, when 0
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The following f(t) is a periodic function of period 2π, defined over the period
0≤t≤ 2T,
:) - lỏ
(2 cos² ()-1, when 0 ≤ t ≤ π,
1o, when
<t≤ 2π.
Express f(t) as a Fourier Series expansion with its Fourier coefficients
ao, an, bn, Vn N, n > 1.
Choose all the correct answers
[]
U
0
an
b₁
2n
z(n²-1)
7
ao
2πT
1
f(t)=sin(t) +
7
- [sin(2t)] = 0
bn = 0
0, when n odd, n = 1,
when n even.
a₁ = 0
a1 =
n=1
Jo, when n odd, n 1,
2n
when n even.
x(n²-1)
an =
1
2
(2n)
T((2n)²-1)
b₁ = 11/22
0 (n/1).
f(t) = =cos(t) + Σ
TL=1
b₁ = 0.
-cos(2nt)
(2n)
T((2n)² - 1)
-sin(2nt)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffdc321a7-0572-4d50-a9f3-8afbf4260389%2F8b132e70-5cd3-4af7-a06d-5d8a741fbf7c%2F3nze9mo_processed.png&w=3840&q=75)
Transcribed Image Text:The following f(t) is a periodic function of period 2π, defined over the period
0≤t≤ 2T,
:) - lỏ
(2 cos² ()-1, when 0 ≤ t ≤ π,
1o, when
<t≤ 2π.
Express f(t) as a Fourier Series expansion with its Fourier coefficients
ao, an, bn, Vn N, n > 1.
Choose all the correct answers
[]
U
0
an
b₁
2n
z(n²-1)
7
ao
2πT
1
f(t)=sin(t) +
7
- [sin(2t)] = 0
bn = 0
0, when n odd, n = 1,
when n even.
a₁ = 0
a1 =
n=1
Jo, when n odd, n 1,
2n
when n even.
x(n²-1)
an =
1
2
(2n)
T((2n)²-1)
b₁ = 11/22
0 (n/1).
f(t) = =cos(t) + Σ
TL=1
b₁ = 0.
-cos(2nt)
(2n)
T((2n)² - 1)
-sin(2nt)
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