Damping forces—a friend or a foe in explaining mechanical motion?

Abstract

This paper presents simple, cheap, easily accessible and, for students, impressive demonstration experiments for three typical examples of physical systems for which damping forces ought to be involved in the equations of motion: a body falling in air, a damped mechanical oscillator, and Foucault currents. The various models of such forces are studied using an elementary physical and mathematical approach. It appears, maybe as a slightly surprising result, that a commonly used model of damping forces in mechanics—air drag force linearly depending on velocity—is not realistic in many typical situations. Equations of motion are solved numerically with standard software packages, even in cases where an analytical solution exists. Thus, the explanation of solved problems is on a level corresponding to an undergraduate university course in general physics. The results of these demonstration experiments are compared with the graphical outputs of numerical solutions.

Coupled rolling motion: considering rolling friction in non-holonomic mechanics

“…Typically, friction is neglected in many topics and related examples of undergraduate theoretical mechanics courses. In textbooks, the simplest problems of a damped harmonic oscillator or pendulum are typically used to present friction phenomena in undergraduate mechanics (recently, these problems have been studied and extended for educational purposes in [2][3][4]; some more advanced problems have recently been solved for students to get a better understanding of the topic; see e.g. [5]).…”