Does the human body (which is basically a collection of more or less loosely coupled, and more or less damped, oscillators) have a "resonant frequency"? Do you have a reference for this?
Yes, it does. All structures do. And yes, I do have a reference -- some are scholarly the other is empirical. Much of the research I have gathered on the issues of vibration, inverted pendulum stability, neuromuscular aspects of reflexes, fascial smooth-muscle-like action, and the relation of oxytocin modulation to the above -- I have made available on Google Docs
for those who are interested in looking at it.
As to that point specifically in the scholarship, this is most directly on point about the human body's resonance range.
... the resonance frequencies of
standing men vary over a wide range from 4 to 16 Hz. ...
And anticipating a followup- yes -- the damping at the limb connections can be varied as well -- but this is a function of where harmonic nodes will be allowed, and as you may see below, the attempt to voluntarily change the damping at the limb segments is exploited by the mechanism that I attribute to aiki to involuntarily alter postural stability.
As to resonance empirically, perform an energetic furitama
with your hands at your hara
and find the frequency that drives your body to bouncing your heels on the mat -- then count the cycles according to stopwatch and find the frequency. It should be about 10 Hz unless you are very large or very small. If you do tekubi furi
over your head, that resonance occurs at ~5Hz, but it feels basically the same.
While the cited work does not speak to the reason for the range or its boundaries, others do, and at least one reason is fairly commonsensical. The body has three major segments, lower limbs, torso and upper limbs -- of roughly equal length. The frequency range noted is roughly based on a ~5Hz module increment of approximately 5-10-15 across those three possible segments. Thus, depending on how the body is disposed to allow harmonic (resonance) nodes to form, the presumed ~5Hz fundamental or first harmonic may be strongest in either a ~5Hz, ~10 Hz (second harmonic) or ~15 Hz (third harmonic) mode across one, two or three segments respectively. A "whole body" (5Hz) action has only terminal nodes. A binary segment (10 Hz) action has one intermediate node at the lower dantien (disregarding the arms). A three segment (15 Hz) action has two intermediate nodes at the lower and upper dantien (upper cross) with the arms as the third segment).
Add another body in connection and nodes may be formed in both the upper or lower dantien of either partner. It creates a set of resonance nodes across a longer set of segments and which may be driven by a resonance to subdivide itself similarly. Resonance creates a "downhill" -- a low energy posture where the nodes have zero displacement (or equivalently zero stress statically) It takes more energy for the connected structure to NOT adopt the same pattern if there is a resonance involved.
More clever people may note that these segment lengths are not precisely equal, and the length between dantiens is notably shorter than the length of the limbs. But the "viscosity" of the torso is different from that of the lower and upper limbs and may explain some difference in effective length between nodes, because the properties of the transmission medium change between the limbs and the torso. In addition, the point at which the limbs are "shear neutral" under their own weight is where they they are slightly flexed (tegatana
), and thus effectively shorter. In that slightly flexed condition, the elbow and knee joints have almost no surface creases or wrinkles. If the knee is fully straightened, the kneecap is wrinkled (compression) and the back of the knee is stretched taut (tension) together indicating a bending stress and thus a simultaneous shear. The elbow is similar.
I can imagine that the lungs might act as cavity resonators, and I believe that the fluid-filled viscera indeed have a resonance at around this frequency (and hence would respond strongly to furitama), but if you bring in the arms, legs and head (as do most of us) it all gets rather complicated.
No, it is more basic than that -- and has to do with the structural organization of the human frame, the necessity of normal sub-perceptive vertical vibration tone that makes the human structure mechanically stable without any cognitive feedback at all, and spinal reflexive actions in the limbs that serve to protect the body structure from destructive force and are highly sensitive to such manipulation when applied in resonant pulses that drive the structure out of its normal stability regime. Research shows that when this system breaks down due to age adding artificial vibration increases balance stability
Since the source of human (inverted pendulum) stability requires only a basic vertical oscillation of normal tone with no feedback mechanism
-- if he is not prepared or trained to "surf the wave" -- so to speak -- of an applied resonance disturbance, the pure physics of the resonance nodes takes him automatically "downhill" (and unexpectedly) out of his normal and unconscious stability zone -- i.e. -- it creates kuzushi
In my opinion it would be more interesting to ask what the transmission speed would be for mechanical disturbances from the wrists to the spine and from the spine to the feet (and hence derive a a characteristic time for each), and to compare this with the reaction time of the relevant parts of the neuromuscular system.
-- and also linked above, and here
. Speed of the waves doesn't matter -- all waves regardless of frequency or wavelength travel though the same medium at the same speed. The properties of the medium dictate that. But only resonant or harmonic frequencies form fixed point nodes at equal intervals -- and in the case of the human body at the upper and lower dantien.
We do know that the 10 Hz vibration signal screws around with the phase delay
between the the stretch reflex and voluntary motor interaction to a significant degree, and causes seeming paradoxical inversion of expected action. Using a critical frequency would result in the agonist and antagonist muscles being in precisely opposite phase of the vibration (one positive, one negative) -- i.e -- in/yo
). In mechanics, this is a form of shear.
Shear is a mechanical property of all wave or other oscillatory action, and is at the root of the "contradictory forces" (simultaneous tension and compression) and which can operate in 90 degree phase relationships (juji
in aiki. A shear implies an oscillation potential.
This phase difference can be 90 degrees out of phase in time to the basic oscillation -- like pumping a swing . Or it can be 90 degrees out of phase in space (as with torsional shear
) stresses (udefuri
when made dynamic). The reflexive reactions called aiki age
and aiki sage
are premised on the relatively "static" spatial torsion driving postural nodes with the stress equivalent of dynamic resonance -- as in kokyu ho undo -- or dynamically in resonance phased in time with applied pulses -- similarly driving the postural nodes, as with furitama
and tekubi furi
and often directly triggering the extensor (aiki age
) or flexor (aiki sage
)reflexes in the lower limbs.