STUDY OF TWO-DIMENSIONAL COUPLED OSCILLATIONS USING A SMARTPHONE ACCELERATION SENSOR FOR PHYSICS TEACHING

Portable devices have been increasingly introduced in Physics teaching over the past few years. This is the case, for example, of digital cameras, webcams, optical mouse of computers, and wiimote. Among portable devices, smartphones combine many capabilities that become them very promising for Physics teaching experiments. For example, they include a digital camera that can be used for the step-by-step following of physical processes. The microphones of the smartphones have found applications in Physics teaching for analysing acoustic phenomena. Also the smartphone's ambient light sensor has been used to analyse a system of two coupled springs undergoing simple and damped oscillatory motion.

The acceleration sensor of the smartphones has been applied to study one dimension oscillatory systems. In these experiments the mobile phone itself is the body under study. This sensor has been used for the study of oscillations by simple and coupled oscillations in one dimension. The sensor captures the oscillations of the acceleration allowing for the description of free, damped and coupled oscillations.

In this work, the normal modes of a two-dimensional oscillating system have been studied using two smartphone acceleration sensors. For this purpose, a set-up consisting of two smartphones coupled by seven springs between them and to the ends of an air table is used. The normal frequencies derived from the data registered by the mobile phones moving with normal motions, are fitted to the harmonic oscillation equation. The four normal frequencies resulting from the fitting are used to fit an arbitrary oscillation with a good agreement in the fit. These experimental frequencies are also fairly compared to the normal frequencies derived from the Dynamical Matrix of the system, yielding a good agreement.

This system is suitable for the study of oscillations in two dimensions in the laboratory of Physics for first and second year students of engineering. In addition, the propose set-up in this work is much cheaper compared to available commercial devices, and so easily implementable in the Physics laboratory.