Modeling a real pendulum with smartphone sensor technology
TSG 21: Mathematical applications and modelling in the teaching and learning of mathematics
Smartphones are often considered to pose a threat to education, yet some of their features provide valuable benefits to solving mathematical modeling problems. New smartphone sensor technology allows to test mathematical models of physical systems in the classroom. This feedback from real measurements can be used to improve and refine the mathematical model, thereby completing the modeling cycle. We present an example where we use a smartphone as a pendulum bob and indirectly measure the elongation angle with the smartphone's built-in acceleration sensors. A spreadsheet implementation of the classical Runge-Kutta algorithm is then used to compute approximate solutions of the differential equation representing the swinging pendulum. Numerical analysis of differential equations is a characteristic and essential element of applied mathematics in science and industry that should get more attention in school mathematics. Assisted by technology, solving real-world problems is absolutely achievable and could be very motivating for students.