This Demonstration compares the motions of two well-known one-dimensional isochronous oscillators, in a simulation using analytical expressions for . One of the potentials considered is parabolic (harmonic) and the other is sheared (anharmonic) [1,2,3]. You can obtain the time-evolution using analytic solutions for the second potential. For simplicity, dimensionless units are used, with mass set equal to 1. Arrows are shown to represent the forces. Students are encouraged to modify the simulation in order to obtain animations for modified energies. They can thus verify the isochronicity of the sheared potential, which follows from the solution .

[1] C. Antón and J. L. Brun, "Isochronous Oscillations: Potentials Derived from a Parabola by Shearing," American Journal of Physics, 76(6), 2008 pp. 537–540.

[2] A. B. Pippard, The Physics of Vibration, Vol 1., Cambridge, UK: Cambridge University Press, 1978.

[3] T. W. B. Kibble and F. H. Berkshire, Classical Mechanics, London: Imperial College Press, 2004.