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Here's what I think:

 

Recording the time for several complete oscillations (usually 10-20) is to minimize the error arising from human reaction time (delay between the time the pendulum actually starts and/or stops moving and the time you start and/or stop your stopwatch), which is usually around 0.2 seconds. This error is always present and one way to minimise it is by doing several complete oscillations.

 

For example, if you only do 1 complete oscillation, which -let's say- take around 2.0 seconds as indicated in your stopwatch, the ACTUAL time taken for 1 oscillation might be around 1.6 seconds, taking into account the delay start/stop time due to delay in human reaction (0.2 seconds delay when you start and 0.2 when you stop). Then the data is not accurate as the error is very large (0.4 out of 2.0)

 

Hence, to minimize (not completely eliminate though) the error, we need to do several complete oscillations. Let's say we take 20 oscillations and end up getting 40.0 s, then we will get the period as 2.0 s but the actual period (if human reaction error is not present) might be (40.0-0.4)/20 = 1.98 s. Thus, the result deviates only slightly from the actual time taken and it is thus better NOT to do only one complete oscillation.

 

I hope my explanation is useful and clear. Hope my english is not confusing as well :p

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