Design and Testing of a Smartphone-Based Damped and Forced Vibration Apparatus Using Phyphox

Abstract

Damped and forced vibrations are important topics in university-level mechanics, but their dynamic behaviour is often difficult for students to understand through static diagrams and mathematical derivations alone. This study describes the design and testing of a smartphone-based experimental apparatus for demonstrating damped and forced vibrations using the Phyphox application and time-of-flight depth sensing. The apparatus consisted of an air track, a slider, springs, a square tank, a salt damping medium, a reciprocating motor, and two smartphones for measuring displacement and driving frequency. The damping condition was adjusted by changing the immersion depth of plastic rods in the salt layer, enabling observation of underdamped, critically damped, and overdamped responses. Forced vibration was investigated by varying the driving angular frequency generated by the reciprocating motor. The measured natural angular frequency of the system was 5.59 rad/s, whereas the value calculated from the spring constant and system mass was 5.80 rad/s, giving a relative error of 3.8%. Under resonant conditions, the external angular frequency was approximately 5.57 rad/s, with a relative difference of 0.36% from the measured natural angular frequency. The results show that the apparatus can visually demonstrate amplitude decay, transitions between damping regimes, and resonance behaviour. The proposed setup provides a practical supplementary tool for mechanics teaching and student experimental activities.