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The motion of the coupled oscillators can be easily calculated on mathematical treatment by applying fast Fourier Transforms (FFT). The FFT showing the motion of the strongly coupled and weakly coupled pendulums are presented.

An example to illustrate that without supporting analysis, a numerical simulation may lead to incorrect conclusions is discussed. A pedagogical example of failure of Runge-Kutta-Felberg (RKF) algorithms for a simple dynamical system that models the coupling of two oscillators is described.

A computer program is described for numerical simulation of one-dimensional oscillators and mappings suitable for use in classes ranging from introductory dynamics to more advanced nonlinear dynamics. Properties of the algorithms used for integrating the equations of motion are discussed as well as some of the interesting physics that can be studied, giving illustrations produced with the program.

Many introductory physics text books fail to discuss the relationship between initial conditions and arbitrary constants for damped oscillators' equations of motion, leading to misconceptions between damped and undamped motion. If initial conditions are not discussed, then conclusions about the oscillatory curves for damped oscillators may be reached by students that do not reflect the fact that omega is arbitrarily set at zero, requiring an initial nonzero velocity.