Two of the recent models discussed illustrate limitations of the modeling
process, the limits of applicability.
In the discussion of "derivatives", the model assumes that the release is
discontinuous, but is then used to argue for the continuity of the acceleration
As others have pointed out, if you are going to look at the transition from
rest to "falling" then you have to model the release as a continuous process
with a variable supporting force.
In the discussion of the spring, the usual assumption that the spring is
massless gets you into trouble with arguing about the acceleration of one
end. There is also the problem of the finite speed of propagation of the
forces along the spring.
Of course the original query about the spring misused N3, as has been
remarked.