Better method to measure the time period of a pendulum
The issue with measuring at the ends is that the pendulum “dwells” at the end point as it turns around, so that there is a greater spread of time for which it looks “at the extreme point” than for which it looks “at the midpoint”.
This spread of time introduces error, whether you are triggering a stopwatch by hand or having some kind of sensor make the decision.
If you tried recording all of the points and determining the period, you’d get the same result — either you take the time between zero crossings of the position, or you take the time between peaks. To get the time between peaks, you need to take a derivative of the position measurement and find its zero crossings, and taking the derivative of a set of data points introduces error.
To measure the time period it is useful to use a fiducial (reference) mark which in this case could be a vertical line drawn on a piece of card and placed “behind” the pendulum bob/string.
It is assumed that the time for a number of complete oscillations will be measured to enable one to find a more accurate value of the period than just measuring the time of just one complete oscillation.
If the fiducial mark is placed at an extreme of the motion of the bob then one can estimate when the bob reaches that mark to start and stop the timer.
However because the amplitude of motion of the bob will decrease with time the estimation of exactly when the bob stops will become progressively more difficult as the position at which this happens can only be guessed.
Even a small error in the location of the position of the bob will result in a relatively large error in the timing because the bob/string would be moving slowly.
Putting the fiducial mark at or near the centre of an oscillation does not require any estimate of when the bob (or string) passes across the fiducial mark as the bob/string will always pass the fiducial mark. Also because the speed of the bob/string is a maximum at this position the error in taking a reading when the bob/string is not quite passing the fiducial mark is going to be relatively small.
An order of magnitude calculation to estimate the possible error in the measurement of a time interval when the bob has not quite reached the fiducial mark by $1\,\rm mm$ at the centre and extreme of a swing..
A simple pendulum of length of $1$ metre has a period of approximately $2$ seconds so $\omega \approx 3 \,\rm s^{-1}$.
For an angular swing of about $5^\circ$ the amplitude of motion is approximately $160$ mm.
Approximating the motion of the bob to a straight line gives an equation for the displacement in millimetres $x = 100\sin (3\,t)$ where the displacement is zero when time $t=0$.
For the bob to move from $x=0\,\rm mm$ to $x=1\,\rm mm$ takes approximately $0.003\,\rm s$ and to move from $x=99\,\rm mm$ to $x=100\,\rm mm$ takes approximately $0.05\,\rm s$.
The reason is that it is (supposedly) marginally easier to judge when the pendulum sweeps past a point when it is moving quickly than when it is moving slowly. In think the point is debatable if you are judging it by eye and manually triggering a stop watch, as your own reaction time comes into play. What's much more important is to measure the elapsed time taken for a very large number of oscillations together, rather than individually, and take the average--that way you can greatly reduce the error associated with judging the exact start and end points.