{"title":"圆柱中活塞的振动及其近似解","authors":"Y. Kajiyama","doi":"10.1142/s2661339521500116","DOIUrl":null,"url":null,"abstract":"We discuss the oscillation of a piston in a cylinder with various amplitudes in adiabatic processes. When a piston in a cylinder moves due to the pressure of a contained ideal gas, it will oscillate like a harmonic oscillator in the case of small amplitude. However, it is difficult to obtain an analytic solution of the equation of motion because of its nonlinearity in general. In this paper, we find that analytic solutions are expressed by elementary functions under approximations of various amplitudes, which can well describe the motion of the piston. It will help students to understand a nonlinear equation of motion appearing in thermodynamics.","PeriodicalId":112108,"journal":{"name":"The Physics Educator","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Oscillation of a Piston in a Cylinder and Its Approximate Solutions\",\"authors\":\"Y. Kajiyama\",\"doi\":\"10.1142/s2661339521500116\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We discuss the oscillation of a piston in a cylinder with various amplitudes in adiabatic processes. When a piston in a cylinder moves due to the pressure of a contained ideal gas, it will oscillate like a harmonic oscillator in the case of small amplitude. However, it is difficult to obtain an analytic solution of the equation of motion because of its nonlinearity in general. In this paper, we find that analytic solutions are expressed by elementary functions under approximations of various amplitudes, which can well describe the motion of the piston. It will help students to understand a nonlinear equation of motion appearing in thermodynamics.\",\"PeriodicalId\":112108,\"journal\":{\"name\":\"The Physics Educator\",\"volume\":\"50 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Physics Educator\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s2661339521500116\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Physics Educator","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s2661339521500116","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Oscillation of a Piston in a Cylinder and Its Approximate Solutions
We discuss the oscillation of a piston in a cylinder with various amplitudes in adiabatic processes. When a piston in a cylinder moves due to the pressure of a contained ideal gas, it will oscillate like a harmonic oscillator in the case of small amplitude. However, it is difficult to obtain an analytic solution of the equation of motion because of its nonlinearity in general. In this paper, we find that analytic solutions are expressed by elementary functions under approximations of various amplitudes, which can well describe the motion of the piston. It will help students to understand a nonlinear equation of motion appearing in thermodynamics.
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