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.
On the Probability Densities of the Output of Some Random Systems
Division of Engineering Sciences, Purdue University, Lafayette, Ind.
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Kozin, F. (June 1, 1961). "On the Probability Densities of the Output of Some Random Systems." ASME. J. Appl. Mech. June 1961; 28(2): 161–164. https://doi.org/10.1115/1.3641646
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