Model Matematika Vibrasi Dawai Dikenai Massa yang Berjalan di Atasnya

Miftakul Janah, Ari Kusumastuti

Abstract

This study discusses the formulation of a mathematical model of string vibration when subjected to mass. There are two variables resulting from the formulation of the model, namely the deflection of the string  and the angle of the string . The deflection of the string  and the angle of the string .  are affected by the friction force, tension force, spring force, and gravity. Then the identification of the working potential and kinetic energy is carried out to obtain the Lagrange equation of the deflection and angle of the string. Based on the formulation steps that have been described, the mathematical model obtained is an ordinary differential equation of the order of one to the power of two. Furthermore, the model is calculated numerically by assigning values to the parameters involved. So it is known that with a string mass of 0.005 kg, 0.05 kg, 0.5 kg, a string mass of 0.075 kg, and an object radius of 0.07 m, it is known that the deflection of the string  is greater if the object's mass is greater. While the angle of the string is in a state of equilibrium before being subjected to a mass and experiencing vibration after being subjected to a mass.

Keywords

Model Building; Mass; String Model; Mathematical Model; String Vibration

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References

Widowati dan Sutimin. 2007. Buku Ajar Pemodelan Matematika. Semarang : FMIPA Universitas Diponegoro.

Pagalay, Usman. 2009. Mathematical Modelling. Malang : UIN Maliki Press.

Zadrak Ndii, Meksianis. 2018. Pemodelan Matematika. Yogyakarta : CV Budi Utama.

D. Young, Hugh, dkk. 2000. Fisika Universitas Jilid II. Jakarta : Erlangga.

Utomo, Pristiadi. 2007. Fisika Interaktif untuk SMA/MA. Jakarta : Azka Press.

Arifudin, M Achya. 2007. Fisika untuk SMA Kelas XII. Jakarta : Interplus.

Yaz, M. Ali. 2007. Fisika SMA Kelas XI. Jakarta : Quadra.

Istiyono, Edi. 2009. Fisika 2 SMP Kelas VIII. Jakarta : Quadra.

Sutresna, Nana, dkk. 2006. Ilmu Pengetahuan Alam untuk Kelas VIII. Bandung :

Grafindo Media Pratama.

Kamajaya. 2007. Ilmu Pengetahuan Alam untuk Kelas VIII. Bandung : Grafindo Media Pratama.

Halliday, D., dkk. 2010. Fisika Dasar Edisi Ketujuh, Jilid II. Jakarta : Erlangga.

Kanginan, Marthen. 2006. Fisika untuk SMA Kelas XI. Jakarta : Erlangga.

Ohene. K. R. 2012. A mathematical model of a suspension bridge-case study: Adomi bridge, Atimpoku, Ghana. Global Advanced Research Journal of Engineering, Technology, and Innovation. Vol 1(3). 047-062.

Anista, Rurin. 2015. Analisis gerak vertikal dawai. Cauchy. 3(4), 188.

Mufid, I., & Kusumastuti, A. 2015. Analisis Dinamik Sudut Defleksi pada Model Vibrasi Dawai. Cauchy, 3(4), 188.

DOI: https://doi.org/10.18860/jrmm.v1i4.14446

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