基于不确定度理论的大摆角单摆平均"周期"测量的最佳累计次数研究
收稿日期: 2019-08-09
修回日期: 2019-10-09
网络出版日期: 2020-03-13
基金资助
陕西师范大学校级教学改革综合研究项目(19JG28,19JG44)资助
The optimum cycles in average“period”measurement of a simple pendulum:A solution based on uncertainty theory
Received date: 2019-08-09
Revised date: 2019-10-09
Online published: 2020-03-13
由于空气阻尼的作用,测量大摆角单摆“周期”时,测量累计次数增加造成平均“周期”不断减小,在无阻尼实验设定下,系统误差随之增大而随机误差却因此减小. 基于弱阻尼大摆角单摆的运动方程与“周期”计算公式,通过数值计算不同摆长与摆角下使不确定度最小的最佳累计摆动次数,发现如果进行单次测量,采用秒表测量时最佳累计摆动次数往往需要大于20 次,采用光电门测量时,在不同的摆长和摆角下,测量次数往往也不止1 次;而如果采用多次测量,则可以显著减小每次测量所需要的最佳累计摆动次数. 采用计算所得最佳摆动次数测量可以将周期测量的不确定度减小到A 类不确定度的√2倍.
凤飞龙, 王公正, 卫芬芬 . 基于不确定度理论的大摆角单摆平均"周期"测量的最佳累计次数研究[J]. 大学物理, 2020 , 39(03) : 32 -35 . DOI: 10.16854 / j.cnki.1000-0712.190363
Due to the damping affected by air,when the average “period”is measured,it would decrease with the accumulated cycles. In the experiment in which zero damping is assumed,this accumulation wouldmake the systematic error increase and the random error decrease,simultaneously. Based on the motion equation and associated “period”formula of the simple pendulum in large-amplitude vibration and weak damping,the optimum accumulated times can be numerically calculated by searching the minimum uncertainty. It has been found that with different string lengths and amplitudes,usually more than 20 cycles should be measured once a time while in some cases when chronograph andphotogateis used,more than 1 cyclesare needed. If the average “period”could be measured for more times,the accumulated cycles in every time could optimally decreased effectively. With the optimal cycles,the uncertainty could get a minimum,about √2 times of the type A uncertainty.
Key words: air damping; large angle amplitudes; systematic error; uncertainty
/
| 〈 |
|
〉 |