摘要
利用机械振动的基本理论以及刚体的相关知识,通过举例分析了非固定轴情况下的刚体系统偏离平衡位置的微振动,剖析错误认知的根源所在,主要问题在于讨论刚体总的机械能时,计算动能部分选择的质心是半球体的球心,而计算势能部分选择半球体的质心,标准不统一所致.利用机械能守恒定律的方法,探讨半球体做简谐振动,仅需大学物理或普通物理学中经典力学知识就可以,降低解析问题的门槛、简化了解题的步骤,避开了用到理论力学中的拉格朗日函数等知识点.通过对错误解答的剖析,有助于加深对刚体、简谐振动等相关基本知识和概念的理解.
Using the basic theory of mechanical vibration and the related knowledge of rigid body,the micro-vibration of rigid body system deviating from the equilibrium position under the condition of non-fixed shaft was analyzed through examples.The root cause of the wrong answer was analyzed.The main problem is that when solving the total mechanical energy of a rigid body,the center of mass selected for the calculation of kinetic energy is the center of the hemisphere,and the center of mass of the hemisphere is selected for the calculation of potential energy.The standard is not uniform.Using the method of the law of conservation of mechanical energy,it is analyzed that the hemisphere is doing simple harmonic vibration.It only needs the knowledge of classical mechanics in college physics or general physics,which reduces the threshold for solving problems,simplifies the steps to solve problems,and avoids the use of knowledge points such as Lagrangian function in theoretical mechanics.Through the analysis,summary and induction of the wrong answers,the understanding of the basic knowledge of rigid bodies and simple harmonic vibrations has been deepened.
作者
赵春然
尹新国
朱孟正
ZHAO Chun-ran;YIN Xin-guo;ZHU Meng-zheng(School of Physics and Electronic Information,Huaibei Normal University,Huaibei 235000,China)
出处
《吉林师范大学学报（自然科学版）》
2022年第1期91-96,共6页
Journal of Jilin Normal University:Natural Science Edition
基金
国家自然科学基金项目(51502106)
安徽省自然科学基金项目(1808085MA08)
安徽省高等学校质量工程项目(2020rcsfjd35,2020SJJXSFK2160)
淮北师范大学质量工程项目(2020xylkc004,kctd19045,jys19082)。
关键词
简谐振动
转动惯量
机械能守恒定律
harmonic oscillation
moment of inertia
law of conservation of mechanical energy
