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

Although the results obtained deviated slightly from the documented values, various sources of errors were discussed to account for the error noted. It was concluded that prior to accurate measurement of the quantities involved and reduction of reaction time during measurement, a more accurate value for gravitational acceleration can be evaluated Displacement of a pendulum from its equilibrium position results in a restoring force that is due to gravitational pull that maintains it in a swinging mode.

The combination of force of gravity and the mass of the pendulum causes it to oscillate constantly about the equilibrium position (Homer & Bowen, 2014). The particular time required to make one complete oscillation is known as the period. Which can also be determined using equation (1) below. Equation 2 above implies that plotting a graph of the square of periodic time T against the length l of the pendulum is a straight line whose gradient is equal to. Using the gradient from the chart, the gravitational acceleration g can be evaluated.

The measurement of error in physical quantities involved is important in determining the accuracy of the results obtained. The error is usually taken as the standard deviation of the measurements. Therefore the error in measurement of length can be determined by equation 3 below Pendulums find many applications in the world including the fact that their regular motion are used to regulate pendulum clocks (Homer & Bowen, 2014). Other applications are typical in seismometers, gravimeters, and accelerometers.

As part of the hypothesis, the experiment seeks to determine the gravitational acceleration based on hypothesis that there is a relationship between the periodic time and length of the pendulum in determining the gravitational acceleration. In this research it is assumed that the amplitude of displacement for each trial is the same. The classic setup, for studying