时间测量中随机误差的分布规律第三组信院三班白潇PB05210258实验目的：用常规仪器（电子秒表等）测量时间间隔，通过对时间和和频率测量的随机分布，学习用统计方法研究物理现象的过程和研究随机误差分布的规律。实验原理：①时间测量仪器的简要原理机械节拍器由齿轮带动摆作周期运动，周期可通过改变摆锤的位置连续调节。②统计分布规律的研究各测量值出现的概率密度分布满足正态分布，其函数表达式为:其中为测量的算术平均值，为测量的标准差,a=,2,3（1）统计直方图方法在一组等精度测量所得N个结果中，先找出其最大值和最小值，求得实验数据的极差R=-,将极差分为K个小区间，每个区间的间隔（）的大小就等于极差R除以K统计测量结果出现在某个小区间的次数称为频数，相对频数称为测定值在该小区间出现的频率，称为累次频率，称为频率密度。若以或或为纵坐标，测量值为横坐标，便可得如下统计直方图。实验仪器：机械节拍器，电子秒表。实验步骤：①设置好机械节拍器，打开机械节拍器。②用电子秒表测量每两个周期所需的时间，记录时间间隔数据。数据处理：1，测量200次，所得数据如下(单位s)R=-=0.77s,可划分小区间数K=8,小区间间隔=0.1s,各区间的量结果的平均值=2.65s；标准差=0.149.3，最大值=3.03s,最小值=2.26s,则极限差频率,相对频率,相对频率密度和累计频率如下表X初始值频数频率累计频率2.20~2.2930.0150.0152.30~2.3920.010.0252.40~2.49250.1250.152.50~2.59420.210.362.60~2.69510.2550.6152.70~2.79440.220.8352.80~2.89200.10.9352.90~2.99120.060.9953.00~3.0910.0051.02.262.542.502.942.662.582.792.76.2.632.662.502.822.462.822.842.562.612.572.672.972.602.692.602.602.872.292.442.732.792.642.422.512.692.552.852.492.782.982.702.782.382.692.532.582.532.342.972.922.942.512.492.622.442.602.602.602.652.712.892.872.632.442.522.462.852.492.702.562.512.652.572.282.792.712.802.462.802.742.872.792.482.572.692.622.792.472.612.692.692.562.452.692.662.542.692.452.692.962.802.792.522.512.772.402.812.512.492.722.712.932.662.622.762.732.892.642.842.712.562.652.492.572.822.732.842.532.752.662.772.672.71.2.622.542.572.782.462.722.862.912.542.652.582.942.792.492.443.032.922.622.692.552.602.762.662.702.712.622.702.642.592.632.572.552.702.612.572.712.582.632.602.762.492.662.472.502.422.562.602.632.612.542.552.772.832.532.702.712.912.782.752.482.762.552.552.542.482.742.792.642.85以频率为纵坐标,测量值x为横坐标,作统计直方图,并将f(x)-x曲线绘在统计直方图中,如上图:测量列的标准差=0.12，测量结果的标准差:==0.0105则两个周期的时间间隔t=()=(2.650.0105)s
