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All Journal Rangkiang Mathematics Journal Jurnal Edukasi dan Penelitian Matematika
Ayuni Kemala Safira
Univeritas Negeri Padang
Education Mathematics Other

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Teori Van Hiele dan Hasil Belajar dalam Bidang Geometri Ayuni Kemala Safira
Jurnal Edukasi dan Penelitian Matematika Vol 8, No 2 (2019): Juni
Publisher : Departemen Matematika

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/pmat.v8i2.6217

Abstract

Geometry is one branch of mathematics that is close to student life, but in reality student geometry learning outcomes are still relatively low. Geometry learning based on the Van Hiele theory is solutions than can help students understand to be better the geometry consept. The purpose of study was to know student geometry learning outcomes who studied with learning based on the Van Hiele theory. The type of research was a quasy experiment with static group design. This research was conducted on class VIII. Sampling was done by using simple random sampling. Data in this research was final test in essay form test which consisted of 6 question, where each question contains indicator of achievement of geometry learning outcomes. The research hypothesis was proven by t test. Based on the result of data analysysis  it is obtained , so it can be cocluded that  student geometry learning outcomes who studies with Van Hiele theory is better than than those who learns with conventional learningKeywords --- geometry learning outcomes, Van Hiele theory, conventional learning.
Analysis of Nonlinear Oscillation Models with External Forcing Using the Multiple Scales Method Safira, Ayuni Kemala; Sa’adah, Aminatus; Sulvianuri, Rani; Agnesia, Yoli
Rangkiang Mathematics Journal Vol. 5 No. 1 (2026): Rangkiang Mathematics Journal
Publisher : Department of Mathematics, Universitas Negeri Padang (UNP)

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24036/rmj.v5i1.138

Abstract

Nonlinear effects accompanied by external forces can cause the behaviour of the system to become more complex and difficult to explain using linear analysis. Therefore, analytical methods are needed to obtain approximate solutions. This paper presents an analysis of approximate solutions to nonlinear oscillation models subject to periodic external forces. The analysis was conducted using the Multiple Scales Method, a perturbation technique for obtaining asymptotic solutions to nonlinear differential equations. This approach is carried out by introducing several time scales and developing solutions as series in ε. The differential equations that model the system are analysed to orders.  and to obtain approximate solutions that describe the oscillation dynamics of the system. The analysis was performed under two main conditions: when the external force frequency approached the system's natural frequency (main resonance) and when the two were not close. In the non-resonance condition, several special cases were also examined: non-resonant, superharmonic resonance, subharmonic resonance, and low excitation frequency. The results show that first-order asymptotic solutions agree well with numerical solutions. The system response is influenced by parameters such as the amplitude and frequency of the external force, as well as the damping parameter. These findings support further research on more complex nonlinear systems and have practical applications in the design of vibration absorbers and rotating mechanical components to control resonance and improve system stability.
Co-Authors Agnesia, Yoli Sa’adah, Aminatus Sulvianuri, Rani