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

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

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Question 1: The solution at x = 1, t = 1 of the partial differential equation Fourier Series and Transform Civil Engineering (CE) Notes | EduRev subject to initial conditions of u(0) Fourier Series and Transform Civil Engineering (CE) Notes | EduRev______.
(a) 1
(b) 2
(c) 4
(d) 6

    [2018 : 2 Marks, Set-I]
Answer: (d)
Solution:
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
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
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
The convergence of the above Fourier series at x = 0 gives
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
    [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
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
Hence, eq. (i), we get,
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
Fourier Series and Transform Civil Engineering (CE) Notes | EduRev

Question 3: The infinite series Fourier Series and Transform Civil Engineering (CE) Notes | EduRev corresponds to
(a) secx
(b) ex 
(c) cos x
(d) 1 + sin2x
    [2011 : 2 Marks]

Answer: (b)
Solution: Fourier Series and Transform Civil Engineering (CE) Notes | EduRev
(By McLaurin’s series expansion)

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