Theoretical, numerical and experimental study about drag force in damped oscillations

A conceptual error is discussed, which concerns the assumption that the drag force is insignificant in damped oscillations, when in point of fact, it is the prevalent component in most practical cases. The problem is posed on theoretical, experimental and numerical bases. On the experimental study, amplitude decrease vs. time is measured in five spring-mass systems, put toghether with spherical bodies of different sizes and densities, and a new method for correcting parallax error is proposed. On the numerical analysis, a damping model is developed with a semiempirical term of variable adjustment. Results present, in general, a very good agreement between experimental data and the numerical model, proving that drag force is the prevalent component in oscillation damping, which agrees with theoretical predictions based on Reynolds number. The lack of discussion of these theoretical bases among introductory physics texts is criticized, and another conceptual error, usually committed in teaching practice, is prevented, which concerns algebraic and graphic procedures for verifying models.

Keywords:
Drag force; Damped oscillations; Numerical calculus