Qassim University
College of Engineering
Mechanical Engineering Department
‫جامعة القصيم‬
‫كلية الهندسة‬
‫قسم الهندسة الميكانيكية‬
Spring Semester (432)
ME 344 (Measurements & Instrumentation)
Individual Assignment #1 (Ch. 1-2) (Due date: Sunday February 20, 2022)
Warning: This is an individual assignment and you should answer all problems by yourself.
1. The following data have the form y=axb. Plot the data in an appropriate format to estimate the
coefficients a and b. Estimate the static sensitivity K at each X.
Y[cm]
0.14
2.51
15.30
63.71
X[m]
0.5
2.0
5.0
10.0
2. The transducer specified in Table below is chosen to measure a nominal pressure of 500 cm H2O. The
ambient temperature is expected to vary between 18 and 25 oC during tests. Estimate the magnitude of
each elemental error affecting the measured pressure.
3. For the Fourier series given by
∞
𝑦(𝑡) = 4 + ∑
𝑛=1
2𝑛𝜋
𝑛𝜋
120𝑛𝜋
𝑛𝜋
𝑐𝑜𝑠
𝑡+
𝑠𝑖𝑛
𝑡
10
4
30
4
Where t is time in seconds.
a) What is the fundamental frequency in hertz and radians/second?
b) What is the period T associated with the fundamental frequency?
c) Express this Fourier series as infinite series containing sine terms only.
Page 1 of 2
Qassim University
College of Engineering
Mechanical Engineering Department
‫جامعة القصيم‬
‫كلية الهندسة‬
‫قسم الهندسة الميكانيكية‬
4. a. Show that 𝑦(𝑡) = 𝑡 2 (−𝜋 < 𝑡 < 𝜋), 𝑦(𝑡 + 2𝜋) = 𝑦(𝑡) has the Fourier series
𝜋2
1
1
𝑦(𝑡) =
− 4 (cos 𝑡 − cos 2𝑡 + cos 3𝑡 + …)
3
4
9
b. By setting 𝑡 = 𝜋 in this series, show that a series approximation for 𝜋 results as
∞
∑
𝑛=1
1
1 1 1
𝜋2
=
1
+
+
+
+
⋯
=
𝑛2
4 9 16
6
5. Construct an amplitude spectrum plot for the Fourier series in Problem 4 for 𝑦(𝑡) = 𝑡 2 . Discuss the
significance of this spectrum for selecting a measurement system.
6. Determine the Fourier series for the function
as shown in the
Figure below. Plot the first, third, tenth and twentieth partial sums of this Fourier series.
Good Luck, Dr. Hesham Othman
Page 2 of 2