In previous papers formulas have been derived describing distribution of a random variable whose values are positions of an oscillator at the moment t, which, in the interval [0, t], underwent the influence of stochastic impulses with a given distribution. In this paper we present reasoning leading to an opposite inference thanks to which, knowing the course of the oscillator, we can find the approximation of distribution of stochastic impulses acting on it. It turns out that in the case of an oscillator with damping the stochastic process ξ t of its deviations at the moment t is a stationary and ergodic process for large t. Thanks to this, time average of almost every trajectory of the process, which is the n-th power of ξ t is very close to the mean value of ξ n t in space for sufficiently large t. Thus, having a course of a real oscillator and theoretical formulae for the characteristic function ξ t we are able to calculate the approximate distribution of stochastic impulses forcing the oscillator.

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 coecient of damping is large and the intensity λ of impulses is small. It is so because the inow 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 λE(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.

Experimental determining of distributions of pulses forcing a linear system, where pulse amplitudes and occurrence instants are random values, is burdened with errors resulting from uncertainty of the measurement and the dierences between the model and the physical phenomenon. The objective of this work is an attempt to minimize these errors through application of an approximation algorithm that allows to determine parameters of response of the system to a single pulse forcing. The conclusions issuing from the investigations indicate that the parameters of the vibrating system should be selected so that the impact of the local deformations that occur while the system is being forced on the parameters of the system response should be as small as possible.

The paper is another step in discussion concerning the method of determining the distributions of pulses forcing vibrations of a system. Solving a stochastic problem for systems subjected to random series of pulses requires determining the distribution for a linear oscillator with damping. The goal of the study is to minimize the error issuing from the finite time interval. The applied model of investigations is supposed to answer the question how to select the parameters of a vibrating system so that the difference between the actual distribution of random pulses and that determined from the waveform is as small as possible.

The motion of an oscillator with damping excited by impulses has the form ξ t = 1 √ a 2 −b 2 0