How to make a theoretical model of a Blackburn pendulum more realistic

[Anthony1]

TL;DR

Improving the theoretical model and practical design of a Blackburn pendulum.

I am modeling a Blackburn pendulum where the bob is much heavier than the string, so I treat the string as massless and inextensible.

I would like to make my model and experiment more realistic. Could you help me with the following questions?

1. How do I formally incorporate linear damping using Rayleigh's dissipation function into the Euler-Lagrange equations?

2. Besides Rayleigh damping, are there any other energy losses or real-world effects (such as air drug...) that are not negligible in a university experiment? And what other negligible influences are there on it?

3. Do you have any practical design suggestions or ideas on how to build an apparatus that allows for easy and precise adjustment of the pendulum's effective lengths?

Thank you for all the answers and suggestions

 

[Baluncore]

Welcome to PF.

https://en.wikipedia.org/wiki/Harmonograph#Computer-generated_harmonograph_figure

 

[tech99]

I presume from a theoretical standpoint that the rotation of Earth will cause the paper to move relative to the pendulum, as per the Foucault Pendulum, but the effect should be negligible.