The accumulator pattern keeps simulations stable in the face of variable frame rate. Accumulate the frame dt into an accum variable. If accum>fixed_physics_dt then step_physics until false. I'm assuming the author did something like that because it's standard practise.

https://www.gafferongames.com/post/fix_your_timestep/

Well, as long as the step rate remains well above the Nyquist limit? Otherwise, your simulation will start to have something akin to aliasing errors.

That is one place where an analytical solution is a benefit, even if it is a bit less realistic. You just have a position(t) parametric function you can evaluate when rendering sporadically.