Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License.
 noun physics The study of
waves in anelastic material
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Examples

Another way to pose the thought experiment is within a single theory that can handle both situations  for instance, elastodynamics.

Ajit, continuing with your bat and ball example, we can calculate the force on the ball by any number of different theories of increasing complexity (analytical dynamics, linear elasticity, nonlinear elastodynamics, etc.) and we will get a different answer for each theory.

In that case, we truly have the same force, but we have a priori decided that we are observing two special cases of a general theory, so there is no way to use these observations to tie two notions of force together  there is only one notion of force, that found in elastodynamics.
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