ANALISIS PERILAKU SOLUSI MODEL GERAK AYUNAN YANG DIPENGARUHI GAYA GESEKAN YANG BERBANDING LURUS DENGAN KECEPATAN SUDUT

Authors

  • Lasker P Sinaga Universitas Negeri Medan

DOI:

https://doi.org/10.24114/jmk.v4i1.11016

Abstract

ABSTRAKModel gerak ayunan yang dipengaruhi gaya gesekan yang berbanding lurus dengan kecepatan sudut merupakan suatu persamaan diferensial nonlinear. Model ini diubah menjadi sistem persamaan diferensial nonlinear yang lebih sederhana dan memiliki solusi bersifat periodik dengan titik kritis  dengan n bilangan bulat. Titik-titik kritis akan  stabil jika n adalah bilangan genap dan sebaliknya, tidak stabil jika n adalah bilangan ganjil. Bentuk kestabilan (simpul, pelana atau spiral) dari titik kritis bergantung pada nilai-nilai parameter model tersebut.Kata kunci: persamaan diferensial, sistem dinamik, gerak ayunan, titik kritis, kestabilan   ABSTRACTThe pendulum motion model influenced by friction force that is directly proportional to the angular velocity. This model is converted into a simpler nonlinear differential equation system and has a periodic solution with critical point  where n is an integer. The critical points will be stable if n is an even numbers and vice versa, will be unstable if n is an odd number. The stability form (node, saddle or spiral) of critical points depends on the value of the model™s parameter.Key words: differential equation, dynamic system, pendulum motion, critical points, stability

Author Biography

Lasker P Sinaga, Universitas Negeri Medan

Departement of Mathematics

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Published

2018-04-01

Issue

Vol. 4 No. 1 (2018): Karismatika

Section

Articles

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