Estimation of the value of gravitational acceleration g based on measurements from a simple pendulum - Essay Example

The experiment entails releasing a mass that is attached at the end of a string with an initial angle (θ). The angle is so small such that the sin θ can be approximated to just θ making this motion to be simple harmonic. It involves swinging the ball for a given number of oscillations and observing the time it takes to make those oscillations. From that information, we can obtain the time per oscillation. This time taken per oscillation is obtained for different lengths of the string. The relationship 4π2/slope is then used to estimate the value of the acceleration due to gravity, g.

The main aim of the pendulum experiment is to determine the effect that the length of the string has on the period taken by the pendulum to make a complete oscillation. It also aims at determining a relationship between the length and the period and also estimating a value for g. The hypothesis for this experiment is that the value for g obtained by any of the experiments available should be approximately equal to 9.8m/s2. The period taken by the pendulum is independent of the mass of the attached object and the initial angle.

The period depends on the length of the string and the acceleration of gravity (Wilson & Hernández-Hall 2009). 3. Set the pendulum swinging through a small angle. Then, measure the time for the period of oscillations (hint: think of a good method here; measuring the period based on a single oscillation might not be a good idea). The analysis involved plotting a graph of T2 against L. since the graph should be linear, the students used simple linear regression to come up with a linear graph. (Michael, Matthew, Gauld, & Stinner 2010).

The results support the objective of the experiment. The students were able to determine the relationship between T2 and L by plotting the graph and obtaining the gradient. Additionally, they were able to compute the value for the acceleration due to gravity, g, with a relative error of