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Fourier Series and Transform Civil Engineering (CE) Notes | EduRev

Topic wise GATE Past Year Papers for Civil Engineering

Civil Engineering (CE) : Fourier Series and Transform Civil Engineering (CE) Notes | EduRev

The document Fourier Series and Transform Civil Engineering (CE) Notes | EduRev is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.

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Question 1: The solution at x = 1, t = 1 of the partial differential equation subject to initial conditions of u(0) ______.
(a) 1
(b) 2
(c) 4
(d) 6
[2018 : 2 Marks, Set-I]
Answer: (d)
Solution:

D’Alembert’s formula,
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
u(x, t) = 3x + 3t
At x = 1, t = 1
u(x, f) = 6

Question 2: The Fourier series of the function,

f(x) = 0, (-π < x < 0 )

f(x) = π - x, (0 < x < π) in the interval [- π, π] is

The convergence of the above Fourier series at x = 0 gives

[2016 : 1 Mark, Set-II]
Answer: (c)
Solution: The function is f(x) = 0,
-p < x < 0
= p - x, 0 < x < π
And Fourier series is,
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
At x = 0, (a point of discontinuity), the fourier series

Hence, eq. (i), we get,

⇒

Question 3: The infinite series corresponds to
(a) secx
(b) e^x
(c) cos x
(d) 1 + sin²x
[2011 : 2 Marks]
Answer: (b)
Solution:
(By McLaurin’s series expansion)

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