American Journal of Physics
Although a simple spring/mass system damped by a friction force of constant magnitude shares many of the characteristics of the simple and damped harmonic oscillators, its solution is not presented in most texts. Closed form solutions for the turning and stopping points can be found using an energy-based approach. A dynamical approach leads to a closed form solution for the position of the mass as a function of time. The main result is that the amplitude of the oscillator damped by a constant magnitude friction force decreases by a constant amount each swing and the motion dies out after a finite time. We present these two solutions and suggest ways that the system can be used in the classroom.
Marchewka, Avi; Abbott, David S.; and Beichner, Robert J., "Oscillator Damped by a Constant-Magnitude Friction Force" (2004). Open Dartmouth: Faculty Open Access Scholarship. 3669.