Damped harmonic oscillator and infinite series

In this work, a quite simple and low-cost experimental arrangement is discussed. Its objective consists of exemplifying in a concrete manner the application of mathematical techniques involving solution by infinite series, destined to the study of determined physical phenomenon. This practice, developed for and directed to undergraduate students taking the course in Mathematics, basically consists of a quantitative study related to the damped oscillatory behavior of a system constituted by a mass coupled to a spring. The experimental results corroborate the phenomenological theory very well and permit the numeric determination of a physical constant normally considered negligible, mentioned only briefly in text books. An important factor in this work refers to the studied oscillatory phenomenon, unlimited in time, but limited in space, which permits an interesting discussion with the students on the concept of mathematical limits.