Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 2, Problem 2.39P
For the even-functioned triangle wave signal defined by
y(f) = (4C/7> + C -T/2 <t <0
y(f) = (-4C/T)t +C0<t<T/2
where C is an amplitude and T is the period,
- Show that this signal can be represented by the Fourier series
/ x 4C(1 - cos nrc) 2jinr v(0 = >5COS --
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
5. Sketch the following function in frequency domain plot:
i. Y(t) = 3 sin (4лt) + 4 cos (4 лt)
ii. Y(t) = 12 sin (10nt) + 5 sin (20лt) + sin (100лt)
Example
m₁ = m₂ = m3 = m.
Solution: The dynamical matrix is given by
[D] = [k]¹[m] = [a][m]
(E.1)
a11
a12
ain
921 922
[k]¯¹ = [a] =
anl an2
Find the natural frequencies and mode shapes of the system shown in the Fig. for k, = k₂ = k3 = k and
F
F(0)
FX(t)
00
me
a2n
Ann
JEET
kr
m₂
k;
ao
Find a false statement regarding the following plot for ()
is the amplitude for the solution z(t) of the equation of motion
+y+wx = ao sin wt.
10
WA(w)
ao
1
Wo
2 0.1
(a) The amplitude wA(w) is the amplitude for the velocity.
(b) At the resonance, the amplitude has the maximum
ag
WA(W)
=
resonance 7
a[wA(w)]
Əw
(d) The resonance is at w = two and twoi.
5
0
=-a0
0.5
0.3 7
ولما
w² - wo
13/2
[(w² - w²)² + 7²w²] ³/2
√(w²z-w²)²+7²
Here, A(w)
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- Problem 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_forwardIf f(x) = x² + cos(x) is a periodic function with period 2W, then a. It is an odd function which gives a value of a = 0 b. Its Fourier series is classified as a Fourier cosine series where a = 0 c. it is neither odd nor even function, thus no classification can be deduced. d. it is an even function which gives a value of b₁ = 0arrow_forward
- Problem 1.3 The signal x(t) is defined as r(t) = 4 cos(wt – -) – 3sin(wt+=). (a) Find the numerical values of A and o to express x(t) as x(t) = A cos(wt +ø). (Hint: Recall phasor addition discussion) (b) Plot all of the phasors from part (a) in the complex plane. Label the plane axes.arrow_forward4. Consider the time-space diagram shown below. For the signals shown, what is the NB bandwidth? а. 15 seconds b. 20 seconds c. 30 seconds d. 60 seconds SIG 4 3,000 SIG 3 2,500 2,000 1,500 SIG 2 1,000 - 500 SIG 1 30 60 90 120 Time (s) Figure. Time-space diagram Distance (ft)arrow_forwardH-W Find Time response for 2S+3 Yes)= s° (s+3)arrow_forward
- Match the transfer function with correct Bode amplitude plots. G(s) = s+ 10 s(+100) s+ 100 G(s) = s(s+10) S G(s)= (s+10) (s+100) (+10) G(s) = (+100) s(+100) G(s) = (+10) (+10)(+100) G(s) = S A. -20 dB/dec 20 dB/dec B. D. 20 dB/dec -20 dB/dec 20 dB/dec -40 dB/dec -20 dB/dec 20 dB/dec 40 dB/dec E. 20 dB/dec -20 dB/dec 20 dB/dec 20 dB/dec -20 dB/decarrow_forward3. Calculate and solve the characteristic equation for the following system: (t) -1 | (t) 0 [ 8 ] *) + 10 [ 17 ] x ) = ( [1] -1arrow_forward2. A spring with k = 4500 N/cm supports a mass of 1.5 Kg. Determine the 'natural frequency' of this system in rad/sec & Hz? 3. Determine the fourier series that represents the function asarrow_forward
- If f(a)= 22 inoLX<4 Lwith periodicity 4, then the value of azin Fourier Series Expansion isarrow_forwardFind the natural frequencies and mode shapes (mode 1 and mode 2) of the system shown in Figure 1 for m₁ = m₂ = 2m and k₁= k₂ = 2k. Base x₁ (1) Figure 1 please help me answer this question now Hand written plz k₁ k₂ 5 +00000 m₁ m₂ x₂ (1)arrow_forwardMagnitude (dB) Phase (deg) The system Bode plots are: -50 -100 -90 -135 -180 -225 -270 10¹ 10⁰ Bode Diagram Frequency (rad/sec) a) The system is stable. b) The system is unstable. c) The system is marginally (critically) stable.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Introduction to Undamped Free Vibration of SDOF (1/2) - Structural Dynamics; Author: structurefree;https://www.youtube.com/watch?v=BkgzEdDlU78;License: Standard Youtube License