弹簧质量对振动系统的影响 修改(1)

玉林师范学院本科生毕业论文

弹簧质量对振动系统的影响The Influence of Spring Quality on Vibration System

院系物理科学与工程技术学院

专业物理学

学生班级2009级2班

姓名戴石贵

学号200905401240

指导教师单位物理科学与工程技术学院

指导教师姓名关小蓉

指导教师职称副教授

弹簧质量对振动系统的影响

物理学2009级2班戴石贵

指导教师关小蓉

摘要

弹簧振子是物理学中的一个典型模型,弹簧振子是指忽略质量的轻弹簧系一物体所组成的系统。在实验中得到的弹簧振子的振动频率和理论结果存在着较大的差异,其中有很多原因,但主要是由于弹簧的质量对振动有一定的影响。人们在讨论弹簧振

m、弹性系数子的振动情况时，往往忽略弹簧本身的质量，实际弹簧振子由质量为

为k的弹簧和连接于弹簧一端质量为m的振动物体组成，为解决实际弹簧振子弹簧质量对振动系统的影响问题，采用研究系统的能量方法，建立了有弹簧质量时系统的动能和势能公式，从不同角度定量的分析了弹簧质量对振动系统的周期之间的影响，该研究对实际振动系统的振动问题具有一定的参考价值和指导意义。

由于弹簧本身有质量，这种弹簧振子不是理想的振子，它的振动周期与弹簧的质量有着密切的联系，当我们把这种影响仅归于质量因素时，振子的周期可以写成与弹簧有效质量有关的表达式，实际上处理这类问题的方法有很多种，像四阶龙格——库塔法、瑞利法、传递矩阵法、求解波动方程法、试探法求解微分方程、机械能守恒近似法、迭代法等等，本文主要运用机械能守恒定律和迭代法分别近似求解实际弹簧振子的周期，并对结果做出详细的讨论。

关键词：弹簧振子，弹簧质量，周期，动能，势能

The Influence of Spring Quality on Vibration System

Physics2009-2Dai Shi-gui

Supervisor Guan Xiao-rong

Abstract

Spring oscillator is a typical model of physics, the spring oscillator means to ignore the quality of the light spring an object composed of system. Experiment spring oscillator frequency of vibration and theoretical results there is a greater difference, there are many reasons, but mainly due to the quality of the spring have a certain impact on the vibration. In the discussion of the spring oscillator vibration case, people tend to ignore the quality of the spring itself, the actual child of spring vibration by the spring-mass for m0, elastic coefficient k for the spring and quality connection on one end of the spring to m vibrating object composition, to address the actual spring oscillator spring-mass vibration system, energy research system, the establishment of the formula of kinetic and potential energy of the spring-mass system, a quantitative analysis of the quality of the spring between the period of the vibration system from different angles, the the actual vibration of vibration problems, the study has some reference value and significance.

Spring quality, this spring vibration sub-vibration sub is not ideal, the quality of its vibration cycle with spring's has close ties, when we put this effect is only attributed to the quality factor, the oscillator cycle can be written as spring-effective quality-related expression, in fact, deal with such issues are many, like Runge - Kutta method, Rayleigh method, transfer matrix method for solving the wave equation method, heuristics for solving differential equations of conservation of mechanical energy approximation , iterative method, etc. In this paper, the use of mechanical energy conservation law and the iterative method of approximate solution to the actual spring oscillator cycle, and the results make a detailed discussion.

Key words：S pring oscillator，Spring-mass，Cycle，Kinetic energy，Potential energy