# Ncku Department Of Mechanical Engineering - Engineering Mathematics II Final Exam

20 Questions | Total Attempts: 142  Settings  Make sure you type your student number into both fields below. I. E. First name = student number, Last name = student number. DO NOT TYPE YOUR NAME INTO THESE BOXES.

• 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. Back to top