damping and damping ratio question

[Armindo Marques]

It is known that an increase in damping can be related with a better capacity of the musculotendinous structures to absorb energy.

However is also known that the absorption of energy is determine by the force a muscle can produce. The distance a muscle must stretch decrease as the force increase.

If we consider that at the beginning of an exercise a muscle is capable to produce higher forces this means that as the force diminish for the musculotendinous structure to absorb the same amount of energy (the same damping coefficient) the musculotendinous structure will have to stretch more. Consider now that from the begin of the exercise the damping ratio increases. The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next.

The question is:
If with a lower force the system will stretch more to absorb the same amount of energy (the time to do this should increase) but the higher damping ratio is telling us that the absorption of energy is occurring more rapidly because the oscillations decay towards zero more rapidly.

This information seems to be somewhat contradictory. How is it possible that this occurs? Or there is any flaw in this rationale?

I appreciate any help.
Kind regards,
Armindo

[Louis DiBerardino]

Re: damping and damping ratio question

Armindo,

Damping is related to velocity rather than position (e.g., stiffness or a spring). Therefore, you could theoretically stretch something so slowly that the viscous damping effects are not present, therefore the energy absorption would be due to the linear stiffness elements of the tissue (if you consider something like the Hill model). Therefore, the absorption of energy due to damping in your two cases above are not necessarily equal.