Theory and Design for Mechanical Measurements
6th Edition
ISBN: 9781118881279
Author: Richard S. Figliola, Donald E. Beasley
Publisher: WILEY
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Chapter 3, Problem 3.41P
A measuring system has a frequency response defined by Af(o). The system has a damping ratio of 0.6 and natural frequency of 1385 Hz. Show how A/(co) varies with frequency. At which frequency does A/(ta) reach a maximum?
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The 8kg body is moved to the right of the equilibrium position and released from rest at time t = 0. The viscous damping coefficient is 23NS/m
and the spring stiffness, K is 38N/m. Determine the damping factor (ratio) of the system.
Note: Give your answer to 3 decimal places.
Other Parameters:
Logarithmic Decrement (8):
Answer:
2ng
2T C
8 = In = In1 = 5 wnTd = 5wn
X2
Xn+1
1-5
wa 2m
k
Damping Ratio (5): 5=
2vkm
2mn
V(21)2+8
Frequency of damped vibration (wa): wa =
1-Wn
Undamped Forced Vibration:
Frequency Ratio (): r-
Xp-x sin w t
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The response of a system 1s given by
x(t) = 0.003 Cos Böt +0.0045in 30t m.
Defermine the amplitude
Og motion, the frequency in Hz, the frequency
in rad/s, the frequency n rpm, the phase angle
and the responce in the form of x(t)= Asn(wk tp)
og mction, the period
4. A convenient way to measure damping in a single-degree-of-freedom system is called logarith-
mic decrement of free response. Consider the free response given by (4). Let's denote t₁ and
t2 denote the times corresponding to two consecutive displacements ₁ and 2 measured one
cycle apart, i.e.,
where
t₂ = t₁ + T
2π
Wd
According to (4), show that the logarithmic decrement dis
T =
x1
8 = log =
x2
where log has base e. Combine (5), (7), and (8) to obtain
= (WnT
8
4π² +8²
Will this method work for other initial conditions? why?
Chapter 3 Solutions
Theory and Design for Mechanical Measurements
Ch. 3 - Prob. 3.1PCh. 3 - Prob. 3.2PCh. 3 - Prob. 3.3PCh. 3 - Prob. 3.4PCh. 3 - A thermal sensor having a time constant of 1 s is...Ch. 3 - Prob. 3.6PCh. 3 - Prob. 3.7PCh. 3 - Prob. 3.8PCh. 3 - Prob. 3.9PCh. 3 - Prob. 3.10P
Ch. 3 - Prob. 3.12PCh. 3 - Prob. 3.13PCh. 3 - Prob. 3.14PCh. 3 - Prob. 3.15PCh. 3 - Prob. 3.17PCh. 3 - Prob. 3.18PCh. 3 - Prob. 3.19PCh. 3 - Prob. 3.20PCh. 3 - A signal of frequency l/rc Hz is passed through a...Ch. 3 - Prob. 3.22PCh. 3 - Prob. 3.23PCh. 3 - Prob. 3.25PCh. 3 - Prob. 3.26PCh. 3 - Prob. 3.27PCh. 3 - Prob. 3.28PCh. 3 - An application demands that a sinusoidal pressure...Ch. 3 - Prob. 3.31PCh. 3 - Prob. 3.32PCh. 3 - Prob. 3.33PCh. 3 - Prob. 3.34PCh. 3 - Prob. 3.35PCh. 3 - Prob. 3.36PCh. 3 - Prob. 3.37PCh. 3 - Prob. 3.38PCh. 3 - Prob. 3.39PCh. 3 - Prob. 3.40PCh. 3 - A measuring system has a frequency response...Ch. 3 - Prob. 3.42PCh. 3 - A catheter is inserted into the vena cava of an...Ch. 3 - Prob. 3.44PCh. 3 - Prob. 3.45PCh. 3 - Prob. 3.46PCh. 3 - Prob. 3.47PCh. 3 - Prob. 3.48PCh. 3 - The displacement of a rail vehicle chassis as il...Ch. 3 - The amplitude spectrum of the time-varying...Ch. 3 - Prob. 3.51PCh. 3 - Prob. 3.52PCh. 3 - Prob. 3.53PCh. 3 - A camera flash light is driven by the energy...Ch. 3 - Run program Temperature Response.vi. The program...
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