Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Textbook Question
Chapter 2, Problem 2.17P
For the Fourier series given by
where t is time in seconds:
- What is the fundamental frequency in hertz and radians/second?
- What is the period T associated with the fundamental frequency?
- Express this Fourier series as an infinite series containing sine terms only.
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QUESTION 4
Consider a 2 DOF system shown below.
k₁
k₂
non
m2
F₁
F
kz
Find the second natural frequency (in rad/s) for the system shown below. Use scientific notation with 3 significant digits. Omit units. (eg. 2.03e0)
Let m1 = 3, m2 = 3, k1 = 4, k2 = 6, and k3 = 8.
Question 3
Find the natural frequency (in rad/sec) of the system in In the figure below:
Use: m1= 5 kg, k1 = 53 N/m, k2 65 N/m and k3 18 N/m
Write your answer to FOUR significant figures. Don't write the units
X1
X2
k1
k2
k3
W ww
m1
The one-dimensional harmonic oscillator has the Lagrangian
L = mx˙2 − kx2/2. Suppose you did not know the solution of the motion, but realized that the motion must be periodic and therefore could be described by a Fourier series of the form
x(t) =∑j=0 aj cos jωt,
(taking t = 0 at a turning point) where ω is the (unknown) angular frequency of the motion. This representation for x(t) defines many_parameter path for the system point in configuration space. Consider the action integral I for two points t1 and t2 separated by the period
T = 2π/ω. Show that with this form for the system path, I is an extremum for nonvanishing x only if aj = 0, for j ≠ 1, and only if ω2 = k/m.
Chapter 2 Solutions
Theory and Design for Mechanical Measurements
Ch. 2 - Prob. 2.1PCh. 2 - Prob. 2.2PCh. 2 - Research and describe the importance of...Ch. 2 - Research and describe the importance of data...Ch. 2 - Determine the average and rms values for the func...Ch. 2 - Prob. 2.6PCh. 2 - Prob. 2.9PCh. 2 - Prob. 2.10PCh. 2 - Prob. 2.11PCh. 2 - Prob. 2.12P
Ch. 2 - Express the function y(t) = 4 sin 2xt + 15 cos...Ch. 2 - Prob. 2.14PCh. 2 - The Fourier series that formed the result for...Ch. 2 - The nth partial sum of a Fourier series is defined...Ch. 2 - For the Fourier series given by where t is time in...Ch. 2 - Determine the Fourier series for the function y(t)...Ch. 2 - Show that y(t) = f2(—jc < t < k), y(t + 2k) = y(t)...Ch. 2 - Find the Fourier series of the function shown in...Ch. 2 - Determine the Fourier series for the function y(t)...Ch. 2 - Determine the Fourier series that represents the...Ch. 2 - Consider the triangle wave shown in Figure 2.26 as...Ch. 2 - Prob. 2.24PCh. 2 - A particle executes linear harmonic motion around...Ch. 2 - Define the following characteristics of signals:...Ch. 2 - Construct an amplitude spectrum plot for the...Ch. 2 - Prob. 2.28PCh. 2 - Sketch representative waveforms of the following...Ch. 2 - Represent the function e(t) = 5 sin 31 At + 2 sin...Ch. 2 - Repeat Problem 2.30 using a data set of 256 num...Ch. 2 - A particular strain sensor is mounted to an...Ch. 2 - Prob. 2.33PCh. 2 - Prob. 2.34PCh. 2 - Consider the upward flow of water and air in a...Ch. 2 - Prob. 2.37PCh. 2 - Prob. 2.38PCh. 2 - For the even-functioned triangle wave signal...Ch. 2 - Prob. 2.40P
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