The code used to numerically simulate a charged pendulum above a grounded conducting surface can be found here.
Some links are below.
Background information on:
Method of Images
The method of images is described at the introductory level in sections 6-7 through 6-9 in the Feynman Lectures vol. II.
Another discussion on the method of images can be found in the open textbook used by UCSD which can be found here.
Harmonic Motion
An introductory description of harmonic motion can be found in chapter 15 of the openstax's University Physics textbook.
A general description of harmonic motion can be found in section 7.3 in the openstax's Calculus textbook.
Numerical Methods
A discussion of Euler's finite difference method of numerically solving differential equations is described in openstax's Calculus textbook.
Numerical solutions are also described in sections 9-5 through 9-7 in the Feynman Lectures vol. I.
Coulomb's Law
Coulomb's law is described in chapter 4 of the Feynman Lectures vol. II.
Coulomb's law is also discussed in section 5.3 of openstax's University Physics.
Python resources can be found: