简谐振动实验中相关物理量间的关系与能量守恒的研究

摘要

It describes how to more accurately measure the speed and period of the slider when doing simple harmonic vibration on the air track,as well as the equivalent mass and stiffness coefficient of the springslinked-with the slider.By utilizing Joly Balance and method of successive minus,the equivalent mass and stiffness co-efficient of three pairs of springs are measured and calculated.The results are in good agreement with those of aforementioned experimentson air track.Based on this,the relationship between physical quantities are quantita-tively investigated and the results show that the cycle of the harmonic vibration is independent of amplitude,the square of the cycle islinearly proportional to the additional counter weight.The systematic error of measured ve-locity is analyzed and conservation of the mechanical energy is verified by multiple sets of experiments while the measured velocity is modified. The relationship between physical quantities and the viariation tendency of energy is vividly demonstrated by using software Origin.This will help students to better understand the law ex-isted in the experiments,and can greatly promote experimental teaching effects.%介绍了如何较为精确地在气垫导轨上测量滑块做简谐振动时的速度、周期、弹簧的等效质量和劲度系数等物理量。利用焦利氏秤对实验中的三对弹簧进行测量，通过逐差法计算得出弹簧的等效质量和劲度系数，其结果和气垫导轨实验所得结论符合较好。在此基础上，对实验中物理量之间的关系进行定量研究，得到周期与振幅无关、周期的平方与滑块的配重块质量呈线性关系。分析了气垫导轨测量速度产生误差的原因，在对测得的速度进行修正后，通过多组实验验证了简谐振动过程中机械能是守恒的。利用Origin软件绘制曲线描述物理量之间的关系和能量变化趋势，生动形象地展示了实验中存在的规律，有利于学生更好地理解实验结论，对实验教学效果有一定的促进作用。