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Complex Analysis and integral transforms — Minor 2 2023 question paper

MMMUT Mechanical Engineering previous year question paper for Complex Analysis and integral transforms (BSM-153), semester 2, Minor 2 2023. All 8 questions are listed below, each with a written answer on Nexsus.

Paper details

  • Subject: Complex Analysis and integral transforms (BSM-153)
  • Branch: Mechanical Engineering
  • Semester: 2
  • Exam: Minor 2 2023
  • Questions: 8

Questions asked in Complex Analysis and integral transforms Minor 2 2023

  1. Q1. Attempt any two parts of the following. Q1 (a) is compulsory.
  2. Q1(a). (i)Solve by the method of Laplace transforms, the equation Y''' + 2Y'' - Y' - 2Y = 0 gives y(0) = y'(0) = 0 and y''(0) = 6 (ii)Find the Laplace transform of e^(-2t)(4sinh3t - 5cosh3t) [5 marks]
  3. Q1(b). Prove that ∫_0^∞ t^3 e^(-2t) sin t dt = 0 [3 marks]
  4. Q1(c). Find the inverse Laplace transform (i) (2s^2 - 6s + 5)/(s^3 - 6s^2 + 11s - 6) (ii) (s^2 - 3s + 4)/s^3 [3 marks]
  5. Q2. Attempt any two parts of the following. Q2 (a) is compulsory.
  6. Q2(a). Find the Fourier transform of f(x) = {1 - x^2, |x| ≤ 1; 0, |x| > 1}. Hence evaluate ∫_0^∞ (x cos x - sin x)/x^3 cos(x/2) dx [4 marks]
  7. Q2(b). An infinite string is initially at rest and that the initial displacement is f(x), (-∞ < x < ∞). Determine the displacement y(x, t) of the string. And also that y(x, t) = 1/2 [f(x - ct) + f(x + ct)] [3 marks]
  8. Q2(c). (i)Solve y_n+2 + 6y_n+1 + 9y_n = 2^n with y_0 = y_1 = 0, using Z-transforms. (ii)Find Z-transform of n sin nθ [3 marks]