We discover the appearance of interesting Cassinian ovals in the motion of a two-dimensional harmonic oscillator. The trajectories of the oscillating points are ellipses depending on a parameter. The locus of the foci of these ellipses is a Cassini oval. The form of this oval depends on the magnitude of the initial velocity.
"Cassini Ovals in Harmonic Motion Orbits." J. Geom. Symmetry Phys. 47 41 - 49, 2018. https://doi.org/10.7546/jgsp-47-2018-41-49