This paper theoretically studies a simple system of two identical linear springs connected symmetrically to a mass in a V-shaped configuration, with an additional adjustable external force applied to the mass. As this force is varied, under certain conditions the equilibrium position of the mass demonstrates strong dependence on the history of changes in the external force, exhibiting hysteresis. Mathematically, variations of the external force cause the system to undergo two saddle-node bifurcations at two differing critical points, leading separately to the creation and destruction of branches of stable equilibria. Analysis of the bifurcation diagram shows that the saddle-node bifurcations cause hysteresis in the system, and the behavior is summarized in a hysteresis graph.

Christopher Ong

American Journal of Physics

美国物理学杂志 (AJP) 的使命是发表有关物理学教育和文化方面的文章，这些文章对物理学学生、教育工作者和研究人员的不同受众来说是有用的、有趣的和可访问的。我们的读者通常会在他们的专业之外阅读，以扩大他们对物理学的理解，并在本科和研究生阶段扩展和增强他们的教学工具包。

The mission of the American Journal of Physics (AJP) is to publish articles related to physics education and culture that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our readers often read beyond their professional fields to broaden their understanding of physics and to expand and enhance their teaching toolkit at the undergraduate and graduate levels.

《American Journal of Physics》（美国物理学杂志，AJP）的使命是发表与物理学教育和文化相关的文章，这些文章对物理学学生、教育工作者和研究人员等不同受众具有实用性、趣味性和可读性。我们的读者通常会在专业领域之外进行阅读，以拓宽他们对物理学的理解，并在本科和研究生阶段扩展和丰富他们的教学工具。

Category	Quartile
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教育学, 学科教育	4
教育学, 物理综合	4

Hysteresis in a simple V-shaped spring-mass system

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Category	Quartile
PHYSICS, MULTIDISCIPLINARY	3