Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) PDF Download

Question 1: The solution at x = 1, t = 1 of the partial differential equation Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) subject to initial conditions of u(0) Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)______.
(a) 1
(b) 2
(c) 4
(d) 6

    [2018 : 2 Marks, Set-I]
Answer: (d)
Solution:
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
D’Alembert’s formula,
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
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 | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
The convergence of the above Fourier series at x = 0 gives
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
    [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 | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
At x = 0, (a point of discontinuity), the fourier series
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
Hence, eq. (i), we get,
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

Question 3: The infinite series Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) corresponds to
(a) secx
(b) ex 
(c) cos x
(d) 1 + sin2x
    [2011 : 2 Marks]

Answer: (b)
Solution: Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)
(By McLaurin’s series expansion)

The document Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Topic wise GATE Past Year Papers for Civil Engineering.
All you need of Civil Engineering (CE) at this link: Civil Engineering (CE)
68 docs

Top Courses for Civil Engineering (CE)

Explore Courses for Civil Engineering (CE) exam

Top Courses for Civil Engineering (CE)

Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev
Related Searches

pdf

,

Free

,

past year papers

,

ppt

,

video lectures

,

Viva Questions

,

Sample Paper

,

Extra Questions

,

Important questions

,

Previous Year Questions with Solutions

,

Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

,

MCQs

,

Summary

,

practice quizzes

,

shortcuts and tricks

,

mock tests for examination

,

Objective type Questions

,

study material

,

Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

,

Semester Notes

,

Fourier Series and Transform | Topic wise GATE Past Year Papers for Civil Engineering - Civil Engineering (CE)

,

Exam

;