An experimental approach to a variable-period damped oscillatory system similar to a bouncing ball and an adaptation to an electromagnetic brake

Abstract

The problem of a ball bouncing in n-hops, despite being a problem extremely easy to observe, is a problem treated by classical mechanics and which, to this day, is without an analytical solution, due to its complexity of mathematical modeling. In this work, we present and discuss experimental measurements for a damped mechanical oscillator that has characteristics identical to the problem of bouncing a ball performing n-hops. Furthermore, we also propose equations to adjust experimental data that behave reasonably within a certain oscillation limit. With the same experiment it is also possible to study rectilinear motion and circular motion, with constant v and $\omega$, this is possible when approaching the experiment with the use of magnetic braking by adding an HD magnet, allowing to determine the speed v of the block during the descent and the angular speed $\omega$ of the rotating disk.

Keywords:
Damped mechanical oscillator; bouncing a ball; magnetic braking