弹性支撑杆下变悬点单摆运动的研究  

Research on single pendulum motion of variable point under the elastic support rod

作　　者：周颖 田蓬勃 李涛[2] 刘瑞丰[2] 刘萍[2] 方爱平 王小力[2] ZHOU Ying;TIAN Peng-bo;LI Tao;LIU Rui-feng;FANG Ai-ping;WANG Xiao-li(School of Electrical Engineering,Xi’an Jiaotong University,Xi’an,Shaanxi 710049,China;School of Physics,Xi’an Jiaotong University,Xi’an,Shaanxi 710049,China)

机构地区：[1]西安交通大学电气工程学院,陕西西安710049 [2]西安交通大学物理学院,陕西西安710049

出　　处：《大学物理》2021年第8期66-71,共6页College Physics

基　　金：教育部高等学校教学研究项目(DJZW201911xb);西安交通大学本科教学改革研究基础课专项(1802Z-04);西安交通大学本科教学改革研究项目(17ZX025,1803Z)资助。

摘　　要：为研究支撑杆为弹性杆时单摆的轴向振荡和切向振荡相互转化这一现象,本文提出基于保守系拉格朗日方程的理论与实验探究方法.分析摆球在不同初始释放角,不同摆线长度以及不同杨氏模量的支撑杆的条件下,在两个垂直方向上振荡的转化时间,以及摆球轨迹和分位移的改变情况.理论与实验结果表明初始释放角越大,转化时间越短;摆长越短,转化时间越短;支撑杆杨氏模量越小,转化时间越短.实验数据与理论结果吻合良好,从理论上很好地解释了实验现象.In order to study the mutual transformation of the axial and tangential oscillations for a simple pendulum when the support rod is an elastic rod,we propose a theoretical and experimental method based on the conservative Lagrangian equation and analyze the transformation time of the pendulum ball oscillating in two vertical directions under the conditions of different initial release angles,cycloid lengths and Young’s modulus support rods,and their influences on trajectory and sub-displacement of the ball.Both theoretical and experimental results show that larger initial release angle,shorter pendulum length and smaller Young’s modulus of the support rod will make the transformation shorter.The experimental result is in good agreement with the theory,and the theory can explain the experimental phenomenon well.

关 键 词：理论力学 拉格朗日方程 进动 弹性杆 

分 类 号：O313.2[理学—一般力学与力学基础]