Harmonic oscillations are isochronous, but so are oscillations in any potential that is shear-equivalent to a harmonic potential. We demonstrate the converse: that every possible isochronous potential is shear-equivalent to a harmonic potential. To do this we show that every potential is shear-equivalent to a unique symmetric potential, and that every isochronous symmetric potential is harmonic. Shearing is thus the only possible period-preserving transformation for potentials with fixed energy.
The American Journal of Physics – American Association of Physics Teachers
Published: Mar 17, 2018
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