Ncku Department Of Mechanical Engineering - Engineering Mathematics II Final Exam

20 Questions | Total Attempts: 142

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Ncku Department Of Mechanical Engineering - Engineering Mathematics II Final Exam

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Questions and Answers
  • 1. 
    What does an Eigenvalue actually mean? Finish this sentence:An Eigenvalue, when subtracted from the diagonals of a matrix,:
    • A. 

      Causes the matrix to be linearly dependent.

    • B. 

      Causes the inverse to be impossible to solve.

    • C. 

      Causes the determinant to be 0.

    • D. 

      All of these statements are correct.

  • 2. 
    What is the determinant of the B matrix?
    • A. 

      0

    • B. 

      5

    • C. 

      11

    • D. 

      None of these are correct.

  • 3. 
    For the matrix shown, compute the eigenvalues and choose them from the list below.
    • A. 

      1

    • B. 

      -1

    • C. 

      5

    • D. 

      -5

    • E. 

      None of these are correct.

  • 4. 
    For the matrix shown, compute the eigenvectors and choose them from the list below.(Choose the most correct answers, you may choose more than one).
    • A. 

      [1, -3]

    • B. 

      [3, -9]

    • C. 

      [1, 1]

    • D. 

      [3, 3]

    • E. 

      All of these are correct.

  • 5. 
    Consider this mass-spring-damper system. Which of the following matrices is a correct description of this system?
    • A. 

      This Equation

    • B. 

      This Equation

    • C. 

      This Equation

    • D. 

      This Equation

  • 6. 
    Consider the Taylor series T(x+a) = T(x) + a*dT/dx + ________ . What is the next term of this series?
    • A. 

      This term

    • B. 

      This term

    • C. 

      This term

    • D. 

      This term

  • 7. 
    Consider the Taylor series T(x-a) = T(x) - a*dT/dx + _______. What is the next term of this series?
    • A. 

      This term

    • B. 

      This term

    • C. 

      This term

    • D. 

      This term

  • 8. 
    Attached here is a code to compute the new temperature T_new using the FTCS method. This is a 1D problem with N cells. Someone believes there are some bugs in this code. Which lines are these bugs on?
    • A. 

      There are no bugs in this code.

    • B. 

      Line 6

    • C. 

      Line 3

    • D. 

      Line 2

    • E. 

      Line 5

  • 9. 
    Consider the 1D bar shown in this figure. The temperature at the left end is fixed (T = 1). The temperature at the right end is fixed (T = 0). If the temperatures T1 to T5 are initially 1, what is the temperature at T3 if we wait until the solution is steady?
    • A. 

      0.5

    • B. 

      0.25

    • C. 

      0

    • D. 

      I don't have enough information.

  • 10. 
    Consider the 1D bar shown in this figure. The temperature at the left end is fixed (T = 1). The temperature at the right end is fixed (T = 0). If the temperatures T1 to T5 are initially 0, the thermal diffusivity is 0.5, what is the temperature at T1 after one time step if dt = 0.15?
    • A. 

      0.6

    • B. 

      0.3

    • C. 

      0.15

    • D. 

      None of these options are correct.

  • 11. 
    Consider the function shown f(x). For the fourier series shown, what is the value of a0?
    • A. 

      This term

    • B. 

      This term

    • C. 

      This term

    • D. 

      This term

  • 12. 
    Consider the function shown f(x). For the fourier series shown, what is the value of an?
    • A. 

      This term

    • B. 

      This term

    • C. 

      This term

    • D. 

      None of these options are correct.

  • 13. 
    Consider the function f(x) shown here. What is the value of bn?
    • A. 

      This term

    • B. 

      This term

    • C. 

      This term

    • D. 

      None of these options are correct.

  • 14. 
    Choose an option below to complete the following sentence: A "periodic function" is a function which:
    • A. 

      Has a period T = 2*pi

    • B. 

      Satisfies the expression f(t+T) = f(t)

    • C. 

      Satisfies the expression f(t+T) = -f(t)

    • D. 

      Has a period T = pi

  • 15. 
    Consider the periodic function shown. What is the value of a0 for this function?
    • A. 

      1

    • B. 

      25/9

    • C. 

      30/9

    • D. 

      None of these solutions are correct.

  • 16. 
    For the function shown here, what is the value of a0 for its Fourier series?
    • A. 

      4

    • B. 

      0

    • C. 

      None of these options are correct.

    • D. 

      2

  • 17. 
    Two bars of some material with length 0.5 initially have temperatures T1 = 5 (left bar) and T2 = 1 (right bar). The thermal diffusivity of the material is 1, and the ends are insulated. Which of the following correctly describes the transient solution?
    • A. 

      This series

    • B. 

      This series

    • C. 

      This series

    • D. 

      This series

  • 18. 
    For the 1D Wave Equation, we may use the method of separation of variables by assuming u(x,t) = A(x)B(t). Using this method, which of the following options is correct for the wave equation?
    • A. 

      A'' + kA = 0 (k = constant)

    • B. 

      B' - CkB = 0 (C, k = constant)

    • C. 

      B'' + CkB = 0 (C, k = constants)

    • D. 

      A'' - kA = 0 (k = constant)

  • 19. 
    Consider the Fourier series shown here. When L = 1, this Fourier series with 3 terms equals f(0.4) = [Blank]. (Fill in the blank space). Use two decimal points - i.e. if your answer = 12.469, type 12.46 in the blank spot. Do not round up or down.
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