From theory to sound: An educational methodology for understanding mechanical vibrations via kalimba design and app-based tuning

This paper presents the design of a laboratory session for engineering students to teach fundamental concepts of mechanical vibrations and eigenmodes using a Kalimba (African thumb piano). The session is structured in three phases: (1) analytical calculation of the natural frequency of each tine, via cantilever beam theory; (2) numerical simulation using finite-element models to refine the design with realistic geometry and boundary conditions; and (3) experimental validation with a physical Kalimba and a custom MATLAB-based spectrum analyzer. This integrated approach allows students to connect theory with practice by developing skills in physical modeling, computational simulation, and spectral analysis applied to a tangible musical object. The proposed session exemplifies both active and project-based learning in vibration education and is presented as a ready-to-implement instructional design.