Abstract:

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