Abstract
A Wilberforce pendulum is a mechanical oscillator often used as an example for the effect of coupling. After establishing a theoretical model of this oscillator and building a prototype, tracking algorithms have been developed to get the position of the oscillator. These tools enable us to highlight the existence of normal modes and determine the constants of the system. We also test different initial conditions to project the state of the pendulum on the normal modes. At the end, we discuss the match between our model and the experimental results. This comparison leads to possible improvements of the model and of the measurements.
Highlights
The Wilberforce pendulum has been named after the British physicist L.R
We present here the development of a convenient toolbox named Measurements of Oscillations by Video Extraction (MOVE) within the framework of our first year physics project at PHELMA [6]
When the amplitude of translation is at one of its peaks, the pendulum does not spin a lot, and vice-versa. This can be explained by the total energy of the system depending on both z and u: its conservation prevents the two motions to reach their peaks at the same time
Summary
The Wilberforce pendulum has been named after the British physicist L.R. Wilberforce, who invented and studied this pendulum at the end of the 19th century [1]. Wilberforce, who invented and studied this pendulum at the end of the 19th century [1] It is a coupled mechanical oscillator composed of a mass suspended to a spring and free to turn around the vertical axis of the system. The motion of the pendulum seems to be disordered. With a closer look, we notice that the pendulum has two motions, the translation and the rotation, whose intensities are linked: when one is very strong, the other is almost nonexistent. Relatively basic and without industrial applications nowadays, this pendulum is an excellent example to grasp the principle of coupling
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