Statistical Characteristics of the Damped Vibrations of a String Excited by Stochastic Forces

Our theoretical study aims at finding some statistic
parameters characterizing the damped vibrations of a string excited by
stochastic impulses. We derive the dependence of these parameters on the
parameters of the string as well as on the stochastic distributions of the
impulse magnitude, and on the place of the action. We also carry out a numerical
simulation verifying the derived mathematical model and interpret the
differences between the results obtained in simulation and the mathematical
calculations. This study is the fourth stage of a research aimed at designing a
probe that facilitates the process of measuring of the parameters, determining
the quality of a technological process.