A student investigated the relationship between the period and the length of a simple pendulum - Leaving Cert Physics - Question 1 - 2017

The student ensured that the pendulum was suspended from a fixed point by using a split cork or two coins that were attached to a stable structure, thus allowing the pendulum to swing freely without any obstruction.

The length of the pendulum was measured from the bottom of the cork or the coins to the middle of the bob.

The most accurate t value is 77.3 s because it has the smallest percentage error when compared to the other values recorded. This suggests that this value represents the closest approximation of the actual period of the pendulum.

To draw the graph, first convert the lengths from centimeters to meters by dividing each by 100. Then, square the period times t for each length to calculate t^2. Plot l (m) on the x-axis against T² (s²) on the y-axis, ensuring that the axes are labeled appropriately.

To calculate g:

1. Determine the slope of the best-fit line through the points on the graph, which represents the relationship between the length of the pendulum and the square of its period.
2. Use the formula for the period of a pendulum: $T^2 = \frac{4\pi^2 l}{g}$
3. Rearranging gives: $g = \frac{4\pi^2 l}{T^2}$
4. Substitute the values derived from the graph into the formula to calculate g, yielding g = 9.8 m/s².