The reason everything gets "shoehorned" into "mass on a spring" is that this is the first term in the Taylor expansion. No matter how ugly an expression you ha

The reason everything gets "shoehorned" into "mass on a spring" is that this is the first term in the Taylor expansion. No matter how ugly an expression you have for force as a function of distance, if you do the Taylor expansion you inevitably get a constant force term (often zero) and a "mass on a spring" term.