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Journal : Transcendent Journal of Mathematics and Applications

Method of multiple scales on Duffing oscillator equation and the existence of its limit cycle Putra, Gusrian; Supmawati, Meysi; Prasetyo, Bayu
Transcendent Journal of Mathematics and Applications Vol 2, No 2 (2023)
Publisher : Syiah Kuala University

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24815/tjoma.v2i2.34035

Abstract

The Duffing Oscillator equation is a second-order nonlinear differential equation that describes an oscillator with a cubic nonlinearity. In this paper, the Duffing equation involves damping factors, restoring forces, periodic force and its frequency, and nonlinearity constants. One of the perturbation techniques that can be used to determine the approximate solution of the Duffing oscillator equation is the method of Multiple Scales. Due to the existence of a sinusoidal periodic force in the equation, the Multiple Scales method produces a sinusoidal approximation as its solution. The solutions are also in a good agreement with the numerical results for small nonlinearity constants. The smaller the nonlinearity constant, the smaller the error obtained with the numerical results in comparison. The approximate solution also tends to be sinusoidal for small nonlinearity constants. Finally, the approximate solution obtained is able to predict the existence of a limit cycle in the Duffing Oscillator equation around the origin due to the existence of its particular solutions.
Co-Authors A.S, Vidinda Maharani Abdillah, Muhammad Adrian Abigael, Rakha AGUS YUDHA PRAWIRA ADISTANA, GDE Agustina, Evania Dwi Aidil, Aidil Aji Prihantoro, Bastian Anas, Abdilah Anik Nur Handayani Aniq Hudiyah Bil Haq, Aniq Hudiyah Bil Antonius Suhartomo Ardiyan, Ardiyan Ayu Ferawati, Ayu Ayu, Dewi Aziz, Faiz Syaikhoni Bin Che Ani, Adi Izhar Budiman, Arianda Damaiarta Tejayanda, Rigger Dari, Marina Ulan Dewa, Refansyah Basu Dewanto, Hendrawan Kusumo Dewi Tamara Diffany Nuzan, Namira Dimas Agung Saputra Djoko Soelistya Elviandri, Elviandri Faisal, Muhamad Agus Faqih, Kamil Figo, Harnando Firmansyah, Iqbal Gustiawan, Putra Chusnul Halawa, Firima Hamka Hamka, Hamka Hanura, Muhammad Ridzky Haya, Dita Alika Fadia Hestiningtyas, Widya I Komang Winatha Imelda Martinelli, Imelda Insan Tajali Nur Jaka Suyana Joni Welman Simatupang Juliannoor, Giovanni Dion Pratama Kalsela, Wanda Frisilia Karnela, Gina Khoir, Mulyanto Abdullah Kiranti, Elza Azizah Malikul Adil Meilika Nadilatasya, Putri Metanoya, Finsri Muhammad Miftah, Muhammad Muhammad Nurcholis Alhadi Nazrin, Mohamad Nining Yuningsih Nisa Rachmah Nur , Anganthi Nisa, Qoiratun Novitasari, Aulia Rahma Nur Azizah Nur Hidayah Nur Rahman, Muhammad Paturu, Reni Oktaviani Pertiwi, Sekar Ayuni Diah Prastyaningrum, Suci Priharta, Ari Primadi, Wahyu Putra, Gusrian Putri, Nanda Belva Kemala Putri, Rhiza Adelia Rahayuningsih, Uut Rasji Riandro Raul, Ignasius Ridlo, Muhammad Abdurrasyid Rofik, Hanifah Nur Rohana, Tatang Roni Herdianto Rosalina, Mira Rosandi, Andri Rosyihuddin, Muhammad Sahirah, Anisa Maulidatus Salas, Jevi Saputri, Novia Ardana Sebastian Matondang, Matthew Mikha Sholichah, Mu'minatus Sofyan Sofyan Sonjaya, Iwan Suen, Mein-Woei Suhana Suhana Sukmawati, Cici Emilia Sunariyo Sunariyo, Sunariyo Supmawati, Meysi Taufiqurrohman, Rifqi Tikaromah, Oom Wahyuni, Nor Alifah Wicaksono Febriantoro, Wicaksono Widoyo, Agus Fatuh Widyatmaka, Burhan Winata, Hari Wuri Handayani Yulianingrum, Aulia Vivi Yulianingrum, Aullia Vivi Zahrah, Mutiara