Penyelesaian khusus persamaan diferensial biasa ordo dua linier tak homogen dengan koefisien konstan untuk fungsi bagian demi bagian
(Particular solution of 2nd order linier non homogeneous ordinary differential equations with constant coefficients for piecewise functions)
Gani Gunawan
Program Studi Matematika, Fakultas MIPA, Universitas Islam Bandung, Bandung, Indonesia
DOI: https://doi.org/10.19184/mims.v24i1.38240
ABSTRACT
Spring mechanical vibration motion system with a damped degree of freedom and influenced by external forces is mathematically expressed as an ordinary differential equation of order of two linear constant coefficients that are not homogeneous. If an external force acts on a stationary system describe as a continuous function 𝑓(𝑡) for any time t, then the system will experience mechanical vibrational motion , which mathematically the equation of motion can be expressed as a superposition. The equation consists of 𝑦ℎ(𝑡) as a solution to a homogeneous form with mechanical vibrations 𝑦𝑝(𝑡) as a solution to a particular form. In terms of the particular solution 𝑦𝑝(𝑡) this article will show a mathematical way when f(t) is a continuous function section by the part which is defined at an interval, such that the mechanical vibration motion equation 𝑦𝑝(𝑡) is at the same time a complete solution 𝑦𝑐(𝑡) of the equation the mechanical vibration system.
Keywords: Vibration, impulse functions, convolution
MSC2020: 34A37
Published
15-03-2024
Issue
Vol. 24 No. 1 2024: Majalah Ilmiah Matematika dan Statistika
Pages
1-11
License
Copyright (c) 2024 Majalah Ilmiah Matematika dan Statistika
