(a) State if the following are True or False. You need not show any working. (i) The period of f(t) = sin(t + n) is T = 2n. 0, -1<
(a) State if the following are True or False. You need not show any working. (i) The period of f(t) = sin(t + n) is T = 2n. 0, -1<
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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Question
already posted for i-iii, need help for iv and v
![1.
(a) State if the following are True or False. You need not show any working.
(i)
The period of f (t) = sin(t + n) is T = 2n.
0 <t <1
(ii) If the function defined over one period is f(t) = { ,"
then ω- π.
-1<t <0°
(iii) If f(t) is odd, then the Fourier coefficients b, # 0 for n = 1, 2, 3, ... because its
integrand f (t) sin nwt is even.
[1+(-1)"]
(iv) E.
sin nt =
=1-sin 2nt .
even
(v) The function f(t) = t³ is periodic over the interval -n <t < n. Its Fourier Sine
2
series coefficient is b, = S", t³ sin nt dt.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb55a038-aa53-4ac6-a34b-5bb8e7b2d991%2Fe644882e-bb74-4816-8181-2718679ff2a5%2Ffh0l8l_processed.png&w=3840&q=75)
Transcribed Image Text:1.
(a) State if the following are True or False. You need not show any working.
(i)
The period of f (t) = sin(t + n) is T = 2n.
0 <t <1
(ii) If the function defined over one period is f(t) = { ,"
then ω- π.
-1<t <0°
(iii) If f(t) is odd, then the Fourier coefficients b, # 0 for n = 1, 2, 3, ... because its
integrand f (t) sin nwt is even.
[1+(-1)"]
(iv) E.
sin nt =
=1-sin 2nt .
even
(v) The function f(t) = t³ is periodic over the interval -n <t < n. Its Fourier Sine
2
series coefficient is b, = S", t³ sin nt dt.
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