On the Probability Densities of the Output of Some Random Systems

[+] Author and Article Information
Frank Kozin

Division of Engineering Sciences, Purdue University, Lafayette, Ind.

J. Appl. Mech 28(2), 161-164 (Jun 01, 1961) (4 pages) doi:10.1115/1.3641646 History: Received March 28, 1960; Online September 16, 2011


The probability density, mean, and variance of the displacement of simple linear one-degree-of-freedom systems are investigated when the spring constants and the initial conditions are random variables. The ensemble mean motion is found to be considerably different from the “mean” motion obtained by first averaging over the spring constants. Furthermore, it is found that only the first and second moments of the initial conditions affect the first and second moments of the displacement.

Copyright © 1961 by ASME
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