Swinburne University of Technology Sarawak Campus

The persisting power of the pendulum

August 19, 2015

By Dr Khameel Bayo Mustapha

The pendulum is a deceptively simple piece of scientific wonder. This seeming simplicity often colour our perception of its behaviour. We are all familiar with the pendulum’s most elementary form – the one formed by attaching a mass to a string or a light rod (the mass is sometimes referred to as a bob). So, for a system this simple it can be very tempting to dismiss its importance. But it turns out that this simple system has a lot to offer. And in this piece, we’ll leap back in time to when the pendulum’s scientific worth first caught the attention of a curious mind, look at its place in the continuum of modern science curriculum, list a few of its variants and wrap up with a few of its extolled applications (from entertainment to oil exploration and in the military). Hop on the seat and swing along gently.

Humankind is a time-addicted creature. Part of our obsession with time stems from the desire to keep tabs on the tide of events as it flows endlessly; from the future, to the present and then to the past. At the beginning of civilization, the sundials – the oldest device used for timekeeping – served this purpose. But the sundial is fraught with inaccuracy, and was later pushed to desuetude by hourglasses and calibrated candles, both of which permit splitting of the day into smaller chunk of time. Nevertheless, none of these improvisations fulfilled the desired precision, and were all later displaced by the pendulum clock. The pendulum’s emergence as a timekeeping device is tied to Galileo, who first observed and analyzed the pendulum’s motion around 1602. It all started, the story holds, when he noticed the swinging of chandeliers in the cathedral of Pisa, in central Italy. Enthralled by what the chandeliers were doing overhead, Galileo resulted to using his pulse to count the period of the swing for different chandeliers. Analyzing his observations, Galileo arrived at conclusions that enabled the scientific quests of many notable minds (e.g. Newton, Hooke and Huygen). His conclusions also remain central to modern scientific enterprise.

Apart from its deployment in clocks, the pendulum is an inexpensive and a superb learning tool for science education and its study remains a routine topic in science literacy. It is taught from elementary to high school and higher education institutions. In elementary and high schools, the study of the pendulum introduces students to foundational ideas: systematic experimentation with physical system; process of scientific inquiry; gravity; inertia; friction and its relationship with energy loss. On the other hand, higher-order cognitive tasks are introduced when the students meet the pendulum in the lower rung of higher education – principally in physics and mechanics courses. At this stage, learning focuses on concepts such as harmonic motion; conservation of energy; energy transformation; vibration control, and many more too numerous to mention. Away from the pure sciences, the pendulum is also courted in social sciences. For instance, its model is a charming mathematical tool in macroeconomics dynamics (an aspect of economics that strives to understand and analyze market instability, economic shock, evolution of business cycles, etc.).

The pendulum exists in many forms. The most common type known to most of us (a mass attached to a string), is technically called a simple pendulum. However, things start to get very interesting as we move from the simple pendulum to its many variants. Let’s examine a couple of its variants. First, the double pendulum. This is formed by attaching one pendulum to another one, resulting in two masses located at reasonable distal lengths along the string. Now, if instead of two masses, we have a single mass suspended by two strings arranged to form a triangle in a vertical plane, then a bifiliar pendulum emerges. A cousin of the bifiliar pendulum is the quadrifiliar pendulum. The playground swing, where you have four vertical strings suspending a seat, typifies a quadrifiliar pendulum. Other examples are the Foucault, spherical and torsional pendula.

The use of pendulum features prominently in many applications. The simple pendulum, for instance, presents an elegant way to determine the universal gravitational constant. It also inspires the design of the playground swing, rocking horse, cable cars, and the metronome. The double pendulum fills a need in sport biomechanics (e.g. to analyze the gait of a gymnast swinging on a horizontal bar). The bifiliar pendulum helps military engineers to measure the mass moment of rockets. The ballistic pendulum is another favorite of the military, and it avails them a simple way to determine the muzzle velocity of projectiles. In oil and gas exploration, the drill-string embodies the behaviour of a torsional pendulum. Further, in many engineering design applications, it is frequently desired to know the resistance of a material to failure from fracture. Scientists called this resistance the fracture toughness. It is determined using the Charpy impact testing machine, which houses a swinging pendulum.

So the next time you see a pendulum, don’t just look at it as a bob attached to a string; see it as a piece of machine that doesn’t bluff, yet is at the heart of many consequential applications.

Dr Khameel Bayo Mustapha is lecturer and researcher with the Faculty of Engineering, Computing and Science at Swinburne University of Technology Sarawak Campus. He is contactable atkbmustapha@swinburne.edu.my