The term, "mesodynamics", as applied to mechanical oscillators, originated in the research of Dr. Peters.  The prefix, "meso" points to the "middle" ground between classical physics on the one hand and quantum physics on the other.  In transitioning from the 19th to the 20th century, physics progressed from the study of systems whose energies were measured in Joules to ones measured in electron volts.  The answer to the following facetious question should be obvious to the reader:  "In a virtually unstudied region whose width is 19 orders of magnitude --a representative difference between  the energies of a classical system and a quantum system, do you suppose there is undiscovered physics of importance?"

The first experiment involving mesodynamics involved a long period pendulum operating at low amplitude.  The purpose of the bell jar surrounding this pendulum was to reduce the influence of air currents.  The jar was not evacuated, since air damping does not contribute significantly to the dissipation of a long period physical pendulum.   Additionally, the knife edge is of secondary importance compared to the dominant damping mechanism, which is the periodic anelastic flexure of the support structure (in this case thinwall stainless tubes under compression and tungsten wires under tension).  

For large amplitudes of the motion, the decay was found to be essentially exponential.  At low levels, it was found to pass through quasi-stationary, metastable states.  A paper describing some of this work is "Metastable states of a low-frequency mesodynamic pendulum", Appl. Phys. Lett. 57 (17), 1825 (1990).

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