This project explores the phenomenon of coupled harmonic oscillators, which have a broad relevance in fields such as mechanics, atomic and quantum physics, optics, electronics, and biology. The paper expands on a model of a harmonic oscillator, using numerical methods for solving differential equations to analyse systems of coupled oscillators. The study focuses on two illustrative cases: a one-dimensional system of two point masses suspended from springs, and a system of two simple pendulums moving in the same plane. The derived mathematical equations of motion provide a comprehensive framework for understanding the behaviour of such systems. Through computational experimentation, the project aims to elucidate the oscillatory behaviour of these systems depending on different parameters and their coupling, particularly focusing on energy transfer between the oscillators. The Runge–Kutta algorithm is employed for solving the initial value problem (IVP) for the ordinary differential equations (ODE) governing these systems. The project underscores the versatility of the harmonic oscillator model by showing that different physical systems can be described by the same mathematical model.