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The study and utilisation of pendulum motion has had immense scientific, cultural, horological, philosophical, and educational impact. The International Pendulum Project (IPP) is a collaborative research effort examining this impact, and demonstrating how historical studies of pendulum motion can assist teachers to improve science education by developing enriched curricular material, and by showing connections between pendulum studies and other parts of the school programme especially mathematics, social studies and music. The Project involves about forty researchers in sixteen countries plus a large number of participating school teachers. The pendulum is a universal topic in university mechanics courses, high school science subjects, and elementary school programmes, thus an enriched approach to its study can result in deepened science literacy across the whole educational spectrum. Such literacy will be manifest in a better appreciation of the part played by science in the development of society and culture.

When identifying instruments that have had great influence on the history of physics, none comes to mind more quickly than the pendulum. Though first treated scientifically by Galileo in the 16th century, and in some respects nearly ‘dead’ by the middle of the 20th century; the pendulum experienced ‘rebirth’ by becoming an archetype of chaos.With the resulting acclaim for its surprising behavior at large amplitudes, one might expect that there would already be widespread interest in another of its significant nonlinearities. Such is not the case, however, and the complex motions of small amplitude physical pendula are barely known. The present paper shows that a simply-constructed metallic rod pendulum is capable of demonstrating rich physics in a largely unstudied area.

The simple pendulum is a model for the linear oscillator. The usual mathematical treatment of the problem begins with a differential equation that one solves with the techniques of the differential calculus, a formal process that tends to obscure the physics. In this paper we begin with a kinematic description of the motion obtained by experiment and a dynamic description obtained by the application of Newton’s laws. We then impose the constraint of compatibility on the two descriptions. This method leads to a fuller understanding of the physics of the oscillator. The paper demonstrates the ubiquity of the linear oscillator as an idealisation of real physical phenomena. It treats the general case of damping with forced motion, including the phenomenon of resonance.

We show that the treatment of pendulum movement, other than the linear approximation, may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are investigated experimentally without limiting amplitudes. By this arrangement new phenomena, the bistability and the jump-effect, can be observed. In the case of bistability the driven gravitational pendulum can oscillate in two different stable modes. Either it oscillates with a small amplitude and approximately in phase with the exciting torque or it oscillates with a larger amplitude and approximately anti-phase. The jump effect is the spontaneous transition from one mode of oscillation to the other. Both effects can be demonstrated and explained.

This paper conveys information about a Physics laboratory experiment for students with some theoretical knowledge about oscillatory motion. Students construct a simple pendulum that behaves as an ideal one, and analyze model assumption incidence on its period. The following aspects are quantitatively analyzed: vanishing friction, small amplitude, not extensible string, point mass of the body, and vanishing mass of the string.

It is concluded that model assumptions are easily accomplished in practice, within small experimental errors. Furthermore, this way of carrying out the usual pendulum experiments promotes a better understanding of the scientific modeling process. It allows a deeper comprehension of those physical concepts associated with model assumptions (small amplitude, point mass, etc.), whose physical and epistemological meanings appear clearly related to the model context. Students are introduced to a scientific way of controlling the validity of theoretical development, and they learn to value the power and applicability of scientific modeling.

In these studies, a vegetable can containing fluid was swung as a pendulum by supporting its end-lips with a pair of knife edges. The motion was measured with a capacitive sensor and the logarithmic decrement in free decay was estimated from computer-collected records. Measurements performed with nine different homogeneous liquids, distributed through six decades in the viscosity η, showed that the damping of the system is dominated by η rather than external forces from air or the knife edges. The log decrement was found to be maximum (0.28) in the vicinity of η = 0.7 Pa s and fell off more than 15 fold (below 2 x 10) for both small viscosity (η < 1 x 10 Pa s) and also for large viscosity (η > 1 x 10 Pa s). A simple model has been formulated, which yields reasonable agreement between theory and experiment by approximating the relative rotation of can and liquid.

Foucault’s pendulum exhibition in 1851 occurred in an era now known by development of the theorems of Coriolis and the formulation of dynamical meteorology by Ferrel. Yet today the behavior of the pendulum is often misunderstood. The existence of a horizontal component of Newtonian gravitation is essential for understanding the behavior with respect to the stars. Two simple mechanical principles describe why the path of oscillation is fixed only at the poles; the principle of centripetal acceleration and the principle of conservation of angular momentum. A sky map is used to describe the elegant path among the stars produced by these principles.

Galileo changed the very concepts or categories by which natural philosophy could deal with matter and motion. Central to these changes was his introduction of time as a fundamental concept. He worked with the pendulum and with the inclined plane to discover his new concept of motion. Both of these showed him that acceleration and time were important for making motion intelligible.

The discovery of the near isochrony of the simple pendulum offered the possibility of measuring time intervals more accurately than had been possible before. However, the fact that it was not strictly isochronous for all amplitudes remained a problem. The cycloidal pendulum provided this strict isochrony and, over a thirty year period from 1659 the analysis of the motion of this pendulum was developed. Newton‘s analysis in his was both elegant and comprehensive and his argument is illustrated in this paper. It provides insights into the revolutionary nature of Newton’s thinking especially compared to the Galilean approach to understanding the motion of the simple pendulum found in early 18th century textbooks.

Teaching Newtonian physics involves the replacement of students’ ideas about physical situations with precise concepts appropriate for mathematical applications. This paper focuses on the concepts of ‘matter’ and ‘mass’. We suggest that students, like some pre-Newtonian scientists we examine, use these terms in a way that conflicts with their Newtonian meaning. Specifically, ‘matter’ and ‘mass’ indicate to them the sorts of things that are tangible, bulky, and take up space. In Newtonian mechanics, however, the terms are defined by Newton’s Second Law: ‘mass’ is simply a measure of the acceleration generated by an impressed force. We examine the relationship between these conceptions as it was discussed by Newton and his editor, Roger Cotes, when analyzing a series of pendulum experiments. We suggest that these experiments, as well as more sophisticated computer simulations, can be used in the classroom to sufficiently differentiate the colloquial and precise meaning of these terms.