Acceleration due to gravity lab series#
The mathematical techniques required to analyze the oscillatory motion of the physical pendulum require the use of Taylor series to approximate a second order nonlinear differential equation to a linear one and the solution of differential equations with constant coefficients using characteristic equations, leading to the transformation of complex exponentials to real-valued functions.įinally, from the experimental physicist perspective, the physical pendulum requires to configure the experiment in order to test the validity of the theoretical approximation, data taking skills and processing, the identification of diverse sources of uncertainty, the ability to choose appropriately the independent and dependent variables to make a plot showing their relationship, the statistical analysis required to fit a model to the data, and the ability to evaluate its reliability (which could lead to the observation of faults in the previous steps).įor some years now, students at our university have been performing the physical pendulum experiment with some success. Blackburn, The pendulum: a case study in physics (Oxford University Press, Oxford, 2005). The main advantages of this experiment are its simplicity, low cost and wealth of both physical and mathematical concepts.įrom the theoretical physics point of view, the physical pendulum can be used to understand the behavior of systems acted on restoring forces proportional to the displacement from the equilibrium point, the concept of a rigid body and the determination of its center of mass (CM) and moment of inertia (and the radius of gyration), the use of Steiner's theorem, the effect of damping, among others G.L. Brittle, Physics Education 47, 537 (2012).], which is generally used to get a measurement of the gravitational acceleration g.
Weltin, American Journal of Physics 32, 267 (1964). The analysis of the oscillatory behaviour of physical systems is a fundamental part of physics courses at the undergraduate level, where simple harmonic oscillators are studied, both from the theoretical and the experimental point of view.Ī very common experiment in fundamental physics courses, which has been used throughout the years, consists on the analysis of the oscillatory motion of a physical pendulum H.
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