So goes my physics limerick. Of course courtesy David Morin of Harvard.
It’s no coincidence that physicists study the harmonic-oscillator potential, kx2/2, so much. A quick application of the Taylor-series expansion shows that any potential looks basically like a quadratic, if you look at a small enough region around an equilibrium point.
A potential may look quite erratic,
And its study may seem problematic.
But down near a min,
You can say with a grin,
“It behaves like a simple quadratic!”