Determining the Distribution of Values of Stochastic Impulses Acting on a Discrete System in Relation to Their Intensity

M. Jabłońskia and A. Ozgab aFaculty of Mathematics and Computer Science, Jagiellonian University, Gołębia 24, 31-007 Cracow, Poland bAGH University of Science and Technology, Faculty of Mechanical Engineering and Robotics, Department of Mechanics and Vibroacoustics, al. A. Mickiewicza 30, 30-059 Krakow, Poland

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In our previous works we introduced and applied a mathematical model that allowed us to calculate the approximate distribution of the values of stochastic impulses ηi forcing vibrations of an oscillator with damping from the trajectory of its movement. The mathematical model describes correctly the functioning of a physical RLC system if the coefficient of damping is large and the intensity λ of impulses is small. It is so because the inflow of energy is small and behaviour of RLC is stable. In this paper we are going to present some experiments which characterize the behaviour of an oscillator RLC in relation to the intensity parameter λ, precisely to λ E(η). The parameter λ is a constant in the exponential distribution of random variables τi, where τi = ti - ti - 1, i = 1, 2, ... are intervals between successive impulses.

DOI: 10.12693/APhysPolA.121.A-174 PACS numbers: 45.10.-b, 45.30.+s