Simulasi Gerak Osilasi Model Pegas Bergandeng Menggunakan Metode Runge-Kutta

Authors

  • Sigid Rahmatullah Prodi Fisika FMIPA Universitas Tanjungpura
  • Yudha Arman Prodi Fisika FMIPA Universitas Tanjungpura
  • Apriansyah Apriansyah Prodi Ilmu Kelautan FMIPA Universitas Tanjungpura

DOI:

https://doi.org/10.26418/pf.v8i3.43681

Abstract

Persamaan gerak sistem pegas bergandeng Fay dan Graham (2003) telah diselesaikan secara numerik untuk kemudian dibandingkan dengan hasil perhitungan analitik. Nilai kesebandingan didasarkan pada Symmetric Mean Absolute Percentage Error (SMAPE). Metode numerik utama yang digunakan untuk menyelesaikan   persamaan gerak model pegas bergandeng adalah Runge-Kutta Orde Empat dan Runge-Kutta 45 Fehlberg sedangkan metode Leapfrog dan Euler digunakan sebagai metode tambahan uji. Ukuran langkah h yang digunakan adalah 0,05 s. Berdasarkan hasil perhitungan dan nilai SMAPE yang diperoleh, Runge-Kutta 45 Fehlberg menjadi metode numerik dengan tingkat ketelitian yang paling baik diantara berbagai metode numerik yang digunakan pada konfigurasi sistem pegas hasil modifikasi model Fay dan Graham (2003) dengan variasi massa m, arah simpangan x, dan besar konstanta pegas k.

Kata Kunci : Pegas, Runge Kutta 45 Fehlberg

References

D. Halliday, R. Resnick dan J. Walker, Fisika Dasar, Jakarta: Erlangga, 2010.

P. A. Tipler dan G. Mosca, Physics for Scientists and Engineers, New York: W. H. Freeman and Company, 2008.

G. C. King, Vibrations and Waves, Chichester: Wiley, 2009.

N. Mufidah dan A. Prihanto, Analisis Sistem Pendulum Sederhana Teredam dengan Simulasi Menggunakan Bahasa Pemrograman Delphi 7.0,†Jurnal Fisika, vol. II, no. 1, pp. 1-5, 2013.

T. H. Fay dan S. D. Graham, Coupled Spring Equations, International Journal of Mathematical Education in Science and Technology, vol. 34, no. 1, pp. 65-79, 2003.

B. Triatmodjo, Metode Numerik Dilengkapi dengan Program Komputer, Yogyakarta: Beta Offset, 2012.

X. Yang dan Y. Shen, Runge-Kutta Method for Solving Uncertain Differential Equations, Journal of Uncertainty Analysis and Applications, vol. 3, no. 17, 2015.

R. N. Darmawan dan R. M. Hariastuti, Analisis Simulasi Solusi Numerik Model Lotka-Volterra dengan Metode Runge-Kutta Fehlberg, Kubik, vol. 3, no. 2, pp. 100-106, 2018.

S. Suparno, Komputasi untuk Sains dan Teknik: Dalam Matlab, 3 penyunt., Jakarta: Universitas Indonesia, 2007.

Alman, Simulasi Komputasi pada Transport Polutan 2 Dimensi dengan Menggunakan Skema Beda Hingga Leapfrog, Jurnal IT, vol. 9, no. 1, pp. 71-76, 2018.

S. C Chapra dan R. P. Canale, Numerical Methods for Engineers, New York: Mc Graw-Hill Education, 2015.

C.Tofallis, A Better Measure of Relative Prediction Accuracy for Model Selection and Model Estimation, Journal of The Operational Research Society, vol. 66, no. 8, pp. 1352-1362, 2015.

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Published

2020-12-15

Issue

Vol. 8 No. 3 (2020)

Section

Articles

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Date: 24-05-2023

Prisma Fisika
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