Leigh thinks he doesn't have many allies on the resonance question. I
think I might be an ally, but I have a couple thoughts that make me
unsure about how far we want to push exact definitions.
I would define "driven oscillation" as a system in oscillation that has
any type of energy input. Whether the source of energy is itself
oscillating or not does not affect this definition.
I would have defined "resonance" as a subset of driven oscillations in
which the energy source has an oscillation at the same frequency as the
oscillator being driven. I believe this basically support Leigh's
statements.
I would have also said that most musical instruments involve driven
oscillations, but not exactly resonance. The violin bow is typically
provided a steady movement; the organ pipe is provided a steady stream
of air, etc.
But now let's look at a commonly described example of resonantly driven
systems... the pendulum clock. How does this differ from the organ
pipe or violin? The force that will be applied to the pendulum of a
good clock is designed to be fairly steady, and the reason the force
seems to be periodically applied is because of an interaction between
the swinging pendulum and the release mechanism for the force. How is
this any different than the interaction of the violin string with the
bow, or the organ-pipe natural frequency interacting with the steady
source of air. The only difference is that the clock escapement is
more mechanically complicated (of course the organ-pipe vortexes might
be more complicated to analyze). Anyway, I don't think the degree of
complication of the coupling between the steady driving mechanism and
the oscillator matters in the definition. In other words I think some
of our accepted examples of resonant oscillation don't meet Leigh's
criteria for resonance.
I don't even think the person pushing the swing qualifies. Assuming I
am a normal person, the energy supplied by the Cheerios I had for br
eakfast is steadily available in the muscles of my arms. A complex
feedback between the swing's motion as observed by my eyes, analyzed by
my brain, and resulting in a timed push effected by my muscles... also
seems to fail Leigh's criteria.
That is, if the driving frequency is determined by the oscillator being
driven, then I think we are observing the non-resonant excitation of
normal modes that Leigh describes, of which aeolian excitation is an
example.
If we want a truly resonant interaction along the lines Leigh is
describing, it seems the frequency of the driver needs to be controlled
independently of the oscillating system being driven. When the
independent driver frequency happens to match the natural frequency of
the oscillator, that's when we have resonance.
I don't know if we want to be that picky about our definitions, but it
seems that's where Leigh's description is headed. I don't necessarily
quarrel with that, but I think it will force use to redefine some of
the "examples" we cite for resonantly driven oscillators, including
clocks and swings.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817