Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781119031703
Author: FIGLIOLA
Publisher: WILEY
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Chapter 2, Problem 2.26P
Define the following characteristics of signals: (a) frequency content, (b) amplitude, (c) magnitude, (d) period.
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me Re
The first natural frequency and corresponding mode shape of the following system are
0,(t)
02(1)
k2
m2= 3.1 , k2=62
Q.5 Use normal mode analysis to find the natural frequencies of the system shown
below:
The specific values of m2 and k2 are given in separate excel sheet.
m2
m¡ = 2 kg
k3=
= 40 N/m
2. Determine the Average and RMS value for the function
y (t) = 25 + 10 sin 6nt
over the time period "O to 0.1" sec Comment on the nature and meaning of
the results in terms of analysis of dynamic signals.
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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- Consider that the free response of the mechanical system is given by y(t) = 5e-at cos(2лƒ) (Eq. 1) whose plot is illustrated in Figure 3: Yh(t) 5 0 0,15 0,25 Arca 0,10 0,20 0,05 0,30 {[s] Figure 3 - Response of the mechanical system as described by Eq. 1. DETERMINE the frequency of damped oscillations of the system in Hertz and rad/s. Considering the damping factor as = 0.075, CALCULATE the system's natural (undamped) frequency. CALCULATE the stiffness of the system if its mass is 25 kg.arrow_forwardProblem 3) The Equations of Motion for a system are given as: [2k -k][X1 + -k 3k. [m1 Where m, =m, m2 =2m a) Determine the frequencies and mode shapes. b) Verify that the natural modes are orthogonal. c) Determine \x2(t)S d) If an excitation force F1(t) = Fo Cosot acted upon the mass m1, Determine the system response.arrow_forwardThe system y(t)=x(t)cos[2(pi)t] is linear time invariant nonlinear time invariant O linear time variant O nonlinear time variantarrow_forward
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