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.Īlso 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.Īn 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.Ī simple pendulum of length of $1$ metre has a period of approximately $2$ seconds so $\omega \approx 3 \,\rm s^$.įor an angular swing of about $5^\circ$ the amplitude of motion is approximately $160$ mm.Īpproximating 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 $t=0$.įor 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 $0.05\,\rm s$. 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.Įven 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. 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. 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. 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.
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