Investigating viscous damping using a webcam

TL;DR

This paper presents a simple webcam-based experiment to analyze viscous damping in harmonic oscillators, allowing viscosity measurement of fluids and suitable for educational settings.

Contribution

It introduces a cost-effective, image processing method for studying viscous damping and measuring fluid viscosity in a classroom environment.

Findings

Measured water viscosity of 1.08 ± 0.07 mPa s, aligning with accepted values.

Demonstrated the method's effectiveness in undergraduate lab settings.

Analyzed underdamped oscillations to extract damping characteristics.

Abstract

We describe an experiment involving a mass oscillating in a viscous fluid and analyze viscous damping of harmonic motion. The mechanical oscillator is tracked using a simple webcam and an image processing algorithm records the position of the geometrical center as a function of time. Interesting information can be extracted from the displacement-time graphs, in particular for the underdamped case. For example, we use these oscillations to determine the viscosity of the fluid. Our mean value of 1.08 \pm 0.07 mPa s for distilled water is in good agreement with the accepted value at 20\circC. This experiment has been successfully employed in the freshman lab setting.