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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
The autocorrelation of the response is then the Fourier transform of the spectral density
R
XX
(τ) =
−∞
1
8π
1
(50 ω
2
)
2
[δ (ω 10) + δ (ω + 10)] e
iωτ
=
1
8π
1
(50 10
2
)
2
e
i10τ
+
1
8π
1
50 (10)
2
2
e
i10τ
=
1
8π
1
(50 10
2
)
2
e
i10τ
+ e
i10τ
=
1
8π
1
2500
2 cos 10τ
=
1
10000
cos 10τ.
168
6.5. Consider equipment to be used in a vibration environment with a white noise acceleration process
having a spectral density S
0
= 49 g
2
s. An electronic unit is modeled as a single degree-of-freedom
system, has a natural frequency of 3 rad/s, and a damping ratio of 0.1. Determine
(a) the
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Publisher Resources

ISBN: 9781439849897