弹簧静变形和重力加速度从固有频率表达式中消失的条件
发布时间：2019-04-16 13:11
【摘要】：教学经常使用固有频率表达式不显含弹簧静变形和重力加速度的振子;但也能找到相反的情形.本研究探讨前者的充要条件.分析发现如果弹簧轴线在质点通过静平衡位置时沿其轨迹的切向,则弹簧静变形从固有频率表达式中消失.在满足这一前提下,进一步要求质点轨迹在静平衡位置的曲率为0,或沿铅垂方向,则重力也无回复力的效果,从而重力加速度在固有频率表达式中不出现.该结论不仅有助于理解重力与固有频率之间的关系,也可指导振动例题编制和选用.
[Abstract]:Natural frequency expressions are often used in teaching not to show oscillators with spring static deformation and gravity acceleration, but the opposite can also be found. This paper discusses the necessary and sufficient conditions of the former. It is found that the spring static deformation disappears from the natural frequency expression if the spring axis follows the tangential direction of the trajectory when the particle passes through the static equilibrium position. Under this premise, the curvature of the particle trajectory in the static equilibrium position is further required to be 0, or along the vertical direction, then gravity has no effect of restoring force, so that the acceleration of gravity does not appear in the expression of natural frequency. This conclusion is helpful not only to understand the relationship between gravity and natural frequency, but also to guide the compilation and selection of vibration examples.
【作者单位】： 中国农业大学理学院;北京联合大学应用文理学院;
【基金】：北京市属高等学校高层次人才引进与培养计划项目(CIT&TCD201404080)资助
【分类号】：O314-4;G642
，
本文编号：2458806
[Abstract]:Natural frequency expressions are often used in teaching not to show oscillators with spring static deformation and gravity acceleration, but the opposite can also be found. This paper discusses the necessary and sufficient conditions of the former. It is found that the spring static deformation disappears from the natural frequency expression if the spring axis follows the tangential direction of the trajectory when the particle passes through the static equilibrium position. Under this premise, the curvature of the particle trajectory in the static equilibrium position is further required to be 0, or along the vertical direction, then gravity has no effect of restoring force, so that the acceleration of gravity does not appear in the expression of natural frequency. This conclusion is helpful not only to understand the relationship between gravity and natural frequency, but also to guide the compilation and selection of vibration examples.
【作者单位】： 中国农业大学理学院;北京联合大学应用文理学院;
【基金】：北京市属高等学校高层次人才引进与培养计划项目(CIT&TCD201404080)资助
【分类号】：O314-4;G642
，
本文编号：2458806
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