Underdamped oscillations of a mass between two springs

Abstract

The oscillations of one mass m suspended between two different springs, assuming a friction force proportional to the velocity ( x ˙ ) , have been studied. For this purpose, an assembly for this system has been made. The movement of the mass is recorded with a smartphone and analysed with Tracker. It is obtained that the graph of the position of the mass m in function of the time is similar to that of an underdamped harmonic oscillator. The registered data with Tracker are exported to Excel and fit to a nonlinear model through the expression x ( t ) = A e − λ t sin ( ω t + α ) . The nonlinear equation of motion is numerically solved with the free Octave package. This solution es very sensitive to the mass of the particle and the stretching of the springs.