Article

TOTAL ENERGY OF HARMONIC OSCILLATOR WITH IMPULSE ACTION

K. ElgondiyevKarakalpak State UniversityS. MatmuratovaKarakalpak State UniversityВ. А. БородинTaras Shevchenko National University of KyivLiudmyla VovkKyiv National University of Culture and Arts

BULLETIN TARAS SHEVCHENKO NATIONAL UNIVERSITY OF KYIV Mathematics Mechanicsjournal2020en

ABI

Abstract

The problem of finding the total energy of a harmonic oscillator with pulsed action at fixed moments of time is considered. Both for the case of the homogeneous equation of harmonic oscillations and for the case of the equation of harmonic oscillations in the presence of external perturbation, formulas for the total energy of the oscillatory system are obtained. The case of periodic impulse effects is analyzed. The conditions under which in this oscillatory system there are periodic modes are specified. It is shown that under the fulfillment of these conditions on the values of impulse action and external perturbation, the total energy of the vibrational system is also a periodic function of the time variable.

Topics

Differential Equations and Boundary Problems Differential Equations and Numerical Methods

Identifiers

DOI: 10.17721/1684-1565.2020.01-41.13.56-59

Citations and references

Cited by 03 references

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