发表机构
Department of Physics, Faculty of Sciences, Universidad de La Serena; Bachelor’s Programme in Astronomy, Faculty of Engineering and Architecture, Universidad Central; Physics Education Laboratory (DFIS-UPLA), Faculty of Natural and Exact Sciences, Universidad de Playa Ancha（拉塞雷纳大学理学院物理系; 中央大学工程与建筑学院天文学学士项目; 普拉亚安查大学自然与精确科学学院物理教育实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过Tracker视频分析自由落体和单摆实验，探究帧率对重力加速度g测量精度和准确度的影响，发现高帧率不一定同时提升两者，其效果取决于系统特性。
AI 中文摘要
本研究探讨了帧率（以每秒帧数FPS表示）对使用Tracker进行视频分析实验估计重力加速度g的影响。分析了两种不同的动力学系统：自由落体和简单单摆。从以120 FPS采集的原始记录出发，通过均匀时间抽取生成了等效的60、30和10 FPS序列，在每次实现中保留了相同的物理轨迹。分析包括自由落体的十次独立实现和单摆的八次实现。对于每种条件，计算了g的平均估计值、各实现间的标准差、相对于g_ref = 9.81 m s^-2的相对误差以及均方根误差（RMSE）。对于自由落体，120 FPS条件表现出最低的离散度和RMSE，而在10和30 FPS下获得的平均估计值更接近参考值。相比之下，对于简单单摆，g的平均值、离散度、相对误差和RMSE在10至120 FPS之间基本保持不变。对10 FPS下12种可能的子采样相位的额外分析表明，这种稳定性并不关键依赖于特定的抽取相位选择，并且与相位相关的变异性相对于各实现间观察到的离散度而言较小。结果表明，较高的时间采样率并不一定同时提供更高的精度和与参考值更接近的一致性。FPS的影响取决于系统的时间特性以及用于估计物理参数的过程。特别是，较高的时间采样密度可能减少离散度或增强对采样的鲁棒性，而不一定产生更接近预期值的估计。
英文摘要
This study investigates the influence of frame rate, expressed in frames per second (FPS), on the experimental estimation of the acceleration due to gravity, g, using video analysis with Tracker. Two different dynamical systems were analysed: free fall and a simple pendulum. Starting from original recordings acquired at 120 FPS, equivalent 60, 30, and 10 FPS series were generated by uniform temporal decimation, preserving the same physical trajectory within each realisation. The analysis included ten independent realisations for free fall and eight for the pendulum. For each condition, the mean estimate of g, the standard deviation across realisations, the relative error with respect to g_ref = 9.81 m s^-2, and the RMSE were calculated. For free fall, the 120 FPS condition exhibited the lowest dispersion and RMSE, whereas the mean estimates obtained at 10 and 30 FPS were closer to the reference value. For the simple pendulum, by contrast, the mean value of g, dispersion, relative error, and RMSE remained essentially unchanged between 10 and 120 FPS. An additional analysis of the 12 possible subsampling phases at 10 FPS showed that this stability does not critically depend on a particular choice of decimation phase and that the variability associated with phase is small compared with the dispersion observed across realisations. The results show that a higher temporal sampling rate does not necessarily provide both greater precision and closer agreement with the reference value. The influence of FPS depends on the temporal characteristics of the system and on the procedure used to estimate the physical parameter. In particular, a higher temporal sampling density may reduce dispersion or increase robustness to sampling without necessarily yielding an estimate closer to the expected value.
Comments15 pages, 3 figures, 1 table
