The paper “ The Pendulum Concept, Angular Displacement, Period of Motion of a Pendulum, Light vs Heavy Pendulums” is a brilliant version of a lab report on physics. A pendulum comprises a mass suspended from a fixed point in such a way that the mass is able to swing freely to and fro. The mass is given a specified displacement and allowed to swing towards the center of the path of motion, which is perpendicularly below the fixed point from which the body is hung as shown in figure 1. Technically, the center of motion is known as the equilibrium position.
Due to the momentum (made up of the mass and the speed of motion of the swinging body), the swinging body passes via the equilibrium position to the other side of the centerline until it reaches the maximum distance it can go on that side. The body then begins its way back via the centerline to the other side of the equilibrium position. The distance the mass moves from one side of the equilibrium position to the other side of the equilibrium position is called the cycle of motion.
The time the pendulum takes to complete one cycle is called the period. This process is repeated while the cycle length, the distance from one extreme of the equilibrium position to the other extreme end, reduces until the body comes to rest at the equilibrium position. Figure 1: A simple gravity pendulum illustrating the principle of pendulums (Parks 2)The pendulum concept has been used for a variety of practical applications. For example, the pendulum principle was applied, by Huygens, to clock mechanisms (Gindikin 83).
The principle of pendulum operation has also been used for measuring seismic activities particularly through the use of the horizontal pendulum seismograph (Wills 106). Most importantly, the equation of pendulum has been used in structural dynamics problems particularly in the determination and prediction of vibrations in mechanical structures (Landis et al. 168). A typical application of the pendulum equation for structural dynamics problems is the determination of breakdown of civil structures, such as roads, buildings, and bridges, arising from external forces, such as earthquakes, automotive, or sudden loading.
Additionally, the pendulum motion can be used to determine how smooth or bouncy a ride can be when certain springs, of given mechanical properties, are used for a given car (Parks 2). Conclusively, the pendulum motion can be used as the basis for analyzing the vibration of complex structures. Some of the properties of a pendulum including period, amplitude, frequency, and length relate in some way. This project is particularly aimed at establishing the relationship between the amplitude and period of a simple pendulum. The establishment of such a relationship is crucial in the various applications of the pendulum because it ensures quality analysis of mechanical vibrations, as well as the quality determination of the various issues determined using instruments using the pendulum concept. Problem StatementIn his experiments, Galileo concluded that there is no relationship between the amplitude and the period of the pendulum (Morgan).
Galileo’ s observations have sparked considerable debate with respect to whether Galileo meant there is no definite relationship between amplitude and period or that there is no significant difference between amplitude and period, which would then mean that period for all amplitudes is the same or differ slightly.
An experiment by Morgan resulted in findings that were against Galileo’ s findings and conclusion as Wright found out that different amplitudes result in different periods. In another experiment by Wright, the findings were different from Galileo’ s and Morgan’ s because Wright observed that were no significant changes in period arising from changes in amplitude for small angles of displacement, particularly for angles below 450. However, the period changes significantly for angles of displacement equal to or more than 450. However, there is no experiment available in the literature, after Wright’ s experiment, which considers the relationship between amplitude and period for angles > 450.
Gindikin, Simon. Tales of Mathematicians and Physicists. Piscataway, NJ: Springer. 2007.
Kirkpatrick, Larry D & Francis, Gregory E. Physics: A World View, 6th Edition. Thomson. 2007.
Landis, Richard., Ertas, Atila., Gumus, Emrah & Gungor F. Free Pendulum Vibration Absorber Experiment using Digital Image Processing. In, D. Adams., G. Kerschen & A. Carrella.
Topics in Non-Linear Dynamics, Volume 3: Proceedings of the 30th IMAC, A Conference on Structural Dynamics. Society of Experimental Mechanics. 2012.
Morgan. Galileo’s Pendulum Experiments. 1995. Web. January 1, 2013,
Parks, James E. The Simple Pendulum. Tennessee University Department of Physics and Astronomy. 2000. Web. January 1, 2013,
Shipman, James T., Wilson, Jerry D & Higgins, Charles A. An Introduction to Physical Science. 13th edition. Cengage Learning. 2011.
Wills, Graham. Statistics and Computing: Visualizing Time: Designing Graphical Representations for Statistical Data. Naperville, Illinois: Author. 2012.
Wright. The Pendulum. N.d. Web. January 1, 2013,
Yin, Cynthia L. How do Varying Amplitudes, Weights, and Lengths Affect the Period of Motion of a Pendulum? California State Science Fair. 2009. Web. January 1, 2013