The period is deemed to be the duration taken for one complete oscillation. The frequency can be deemed to be the number of oscillations that the pendulum can make per unit time the inverse of which is the period i.e. f = 1/T. The amplitude is the longest distance that is traversed by the pendulum in reference to its equilibrium position. The displacement causes the exertion of force that tends to restore the pendulum to its equilibrium position (Nethercott & Walton 2013).
The sum vector of the gravitational force of the mass of the pendulum (mg) and the tension force (T) shown in Figure 1. They constitute the restoring force whose magnitude depends on the displacement from the equilibrium position. Therefore, the restoring force F can be calculated as
The negative sign is an indication that the restoring force is in the opposite direction of the displacement. For small amplitudes, θ is small and therefore θ can be used in place of sinθ. Therefore, the resulting equation is
The aim of this experiment is to estimate the acceleration due to gravity using a pendulum. For purposes of this experiment, the independent variable is the length of the pendulum whereas the period is the dependent variable (Bolton and Bolton 2012).
The table top stand with clamp was placed on a flat working surface. The string was then passed through the pendulum bob and knotted as appropriate to hold the bob in position. The string with the pendulum attached to one end was passed through the split cork, and the length of string adjusted to 0.85m before being clamped onto the retort stand. A Vernier calipers was used to measure the diameter. The length of the string was adjusted to about .8 m. Therefore, the length of the pendulum is l = ls + r .where r is the radius of the bob.
The pendulum was then displaced approximately 5º from its equilibrium position and left to swing back and forth. The time taken for 6 complete oscillations was recorded