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Probabilistic Models for Dynamical Systems, 2nd Edition
book

Probabilistic Models for Dynamical Systems, 2nd Edition

by Haym Benaroya, Seon Mi Han, Mark Nagurka
May 2013
Intermediate to advanced content levelIntermediate to advanced
764 pages
6h 43m
English
CRC Press
Content preview from Probabilistic Models for Dynamical Systems, 2nd Edition
6.15. Consider a single degree-of-freedom system with mass m, damping coefficient c, and no spring
element. The mass is subjected to an excitation force given by m
¨
X(t), where
¨
X (t) is a stationary white
noise random process of intensity S
0
m
2
/s
3
. Determine
(a) the complex frequency response function H(ω) for the response velocity V (t), and
(b) the power spectral density S
V V
(ω) and the mean-square value E{V
2
} of the stationary velocity
response, where V (t) =
˙
X(t).
Solution: (a) From the problem statement, the equation of motion is given by
m
¨
Y (t) + c
˙
Y (t) = mX(t).
Velocity is
˙
Y (t) , and its Fourier transform is iωY (ω) , where Y (ω) is the Fourier ...
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Publisher Resources

ISBN: 9781439849897