Question: With a good stopwatch and some practice, you can measure times ranging from approximately 1 second up to many minutes with an uncertainty of 0.1 second or so. Suppose that we wish to find the period r of a pendulum with r 0.5 s. If we time 1 oscillation, we have an uncertainty of approximately 20%; but by timing several oscillations together, we can do much better, as the following questions illustrate:
(a) If we measure the total time for 5 oscillations and get 2.4 ± 0.1 s, what is our final answer for 7, with its absolute and percent uncertainties? [Remember the rule).
(b) What if we measure 20 oscillations and get 9.4 ± 0.1 s?
(c) Could the uncertainty in r be improved indefinitely by timing more oscillations?