Linear Spring Oscillator with Two Different Types of Damping

This paper presents a simple, cheap and easily accessible demonstration experiment in two modifications. A typical example of a physical system for which damping forces have to be involved into equations is a damped spring mechanical oscillator. Here we use two models of the damping force, being produced by Foucault currents and by the force of the drag in air. It turns out, maybe as a slightly surprising result, that the commonly used model of damping forces in mechanics the air drag force linearly depending on velocity is not realistic in some typical situations. Equations of motion are solved analyticaly, when possible, othervise they are solved numerically. The results of the demonstration experiments are compared with graphical outputs of numerical solutions. Introduction Exercices and problems in bachelor courses of general physics, especially in mechanics, are usually solved and demonstration experiments are usually interpreted assuming that forces originating from the motion of bodies in their enviroment (typically air drag forces) can be neglected. Standard formulations of physical problems and exercices involve such formulations as “suppose that the air drag force is negligible”, “do not take the air drag force into accout”, etc. This leads to a tendency of students to omit damping forces even in situations in which these forces play an essential role. For some mechanical systems a damping force depending linearly on the velocity of the moving body is taken into account. For such a case the equations of motion are often solvable analytically.Unfortunately, the quadratic function of the velocity is more appropriate for describing this force, in many practical cases. Oscilations as a drag force study Experimental motivation We using a usual spring oscillator with a point-like mass. We can verify that the oscilations are practicaly undamped. The damping can be enhanced by adding various damping elements for example an alluminium strip in a magnetic field connected to the oscillator (see Figure.1) or square cartoon plate (see Figure 4). A light-emitting diod is fastened to the mass of the oscillator. The photographs presented in Figure 1 and Figure 4 were obtained by a digital camera placed on a turning tripod. The camera was turned by hand for simplicity and cheapness of the experiment (we wanted to avoid the necessity of an additional equipment and give students themselves a possibility to perform the experiment). This caused some “shaking” of the photograph. On the other hand, as we show later, one can use a particular treatment of the data obtained from the photograph that eliminates these imperfections. Thus, the used experimental simplification does not limit the correctness of experimental results and corresponding conclusions. Technical parameters of the phorograph: equivalent of film sensitivity = ISO 400, diaphragm number = 5, time of exposition = 25 s (30 s, respectively), flash synchronized with the beginning of the exposition time. WDS'05 Proceedings of Contributed Papers, Part III, 649–654, 2005. ISBN 80-86732-59-2 © MATFYZPRESS