In investigating the relationship between the period and the length of a simple pendulum, a pendulum was set up so that it could swing freely about a fixed point - Leaving Cert Physics - Question 1 - 2006

The string must be inextensible to ensure that its length remains constant during the oscillation. This allows for accurate measurements and maintains the conditions necessary for simple harmonic motion (SHM). Any stretch in the string would alter the length and consequently affect the period of the pendulum.

The pendulum was set up by securing one end of the string to a fixed pivot point, allowing the other end to hang freely with the heavy bob attached. To ensure it swings freely, it should be placed between two coins or a split cork. Additionally, care should be taken to minimize air drafts and to ensure the pendulum is in a single vertical plane to avoid interference.

To graph the relationship, plot the square of the period (t²) against the length (l). The expected result is a straight line through the origin, indicating a direct proportionality:

$t^2 ext{ is proportional to } l$

This means that as the length of the pendulum increases, the square of the period also increases, supporting the formula for the period of a simple pendulum, which can be expressed as: T = 2 ext{π} rac{ ext{l}^{1/2}}{g^{1/2}} where T is the period, l is the length, and g is the acceleration due to gravity.