A student investigated the relationship between the period and the length of a simple pendulum - Leaving Cert Physics - Question 1 - 2008

To ensure that the length of the pendulum remained constant while it was swinging, the student used an inextensible string and anchored the pendulum at a fixed pivot point. This method guarantees that the distance from the pivot to the center of mass of the pendulum does not change during the oscillations.

To draw the graph, plot the length of the pendulum (l) on the x-axis and the period for one oscillation (T) on the y-axis, which can be calculated using the formula:

$T = \frac{t}{30}$

After plotting the data points, a straight line should be observed which indicates a linear relationship. According to the theoretical understanding of pendulum motion, the relationship between the period and the length follows:

$T^2 \propto l$

This implies that as the length of the pendulum increases, the period of oscillation increases.

To calculate the acceleration due to gravity (g) from the slope of the graph, use the pendulum formula:

$T = 2\pi \sqrt{\frac{l}{g}}$

By rearranging, the slope can be related to g as:

$g = \frac{4\pi^2 l}{T^2}$

The slope of a graph of $T^2$ versus $l$ gives rac{T^2}{l}, which can be used to find g. Given a slope of approximately 0.247 from the graph,

$g \approx 9.81 \, m/s^2$

This value falls within the expected range for the acceleration due to gravity.