Exploring Fourier series through real life call phone vibrations

Abstract The Fourier series is a fundamental concept in undergraduate physics. It is essential for describing and analyzing periodic phenomena in physics. However, it is often applied only to idealized functions that lack connection to physical situations encountered in daily life. Therefore, there is a need for more contextual examples that demonstrate its relevance to real-life physics phenomena. In addition to their primary role as communication devices, smartphones have evolved into portable tools used in a wide range of physics experiments. An often-overlooked phenomenon in daily life is the vibration of a smartphone upon receiving a call, which presents an opportunity for physics education. This study aimed to analyze the periodic vibrations of a smartphone during incoming calls. Using the Phyphox application, the vibrational behavior was precisely recorded and analyzed, revealing two distinct patterns: constant frequency/period oscillations and harmonic variations. This finding reveals two characteristics of actuators in smartphones. These patterns can be rigorously described using Fourier series representations. The Fourier series expression of the smartphone actuator response has odd and even harmonic coefficients. Everyday phenomena represented in this mathematical function can bridge abstract concepts with real physical phenomena and demonstrate a direct connection with the technology used in smartphones. This study provided a detailed understanding of the periodic vibrations observed in smartphone calls and demonstrated how Fourier analysis can be applied in a familiar context.