Abstract
The characteristics of the first-order probability density function of the response process of a simple oscillator subjected to random impulses occurring at Poisson distributed random times are examined, using Edgeworth's series in conjunction with some results from shot noise theory. The effect of the damping ratio of the system and the rate of impulse occurrence on the shape of the density curve of the response is discussed and it is shown that the distribution has a positive coefficient of excess and a skewness which is dependent on the skewness of the distribution of the impulse strengths. The cases where the impulses are of uniform strength, where they are normally distributed and finally where they are Rayleigh distributed, are examined in some detail.
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