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

The sufficient conditions for the spring's static deformation and gravity acceleration vanishing from the intrinsic frequency expression of a vibrator

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.

Vibration teaching practice employs a plenty of such kind of examples with the gravity and spring＇s static deformation not contributing to intrinsic frequencies. However,there exist indeed counter examples with the gravity and spring＇s static deformation playing a role. We investigate the if-and-only-if conditions for the spring＇s static deformation and gravity acceleration vanishing from the intrinsic frequency expression. Theoretical analysis shows that the spring＇s static deformation vanishes from the intrinsic frequency expression if the spring axis is tan gential to the particle trajectory at the static balance position. With this condition satisfied,the gravity acceleration vanishes from the intrinsic frequency expression if the particle trajectory transgressing the static balance position is either vertical or zero curvature. The conclusion is not only benefit to comprehend the significance of the gravity to the intrinsic frequency,but also useful in compiling and creating new examples for vibration teaching practice.