"Sergey Karavashkin" wrote in message
om...
"George Dishman" wrote in message
...
"Aleksandr Timofeev" wrote in message
om...

For a resonance is indispensable:
- power source;

A pendulum is resonant but contains no power source.

George, excuse me, but this is some inexact. Even mathematical
pendulum needs a source to excite free vibrations.

You are correct of course but being an engineer, I think of that
as the signal source. Aleksandr and I had been talking of RC
oscillators using this as an example:

http://home.earthlink.net/~doncox/wec/Oscillators.html

I understood "power source" to mean the equivalent of the
10V battery supplying the power to replace that lost in the
RC networks. My mistake.

- nonlinear transformer of energy;

A RLC circuit is linear and resonant.

It may sound strange but today the meaning of 'nonlinear system' is
quite fuzzy.

Examples of non-linearity for me would be the transistor in
the circuit above that has an exponential relation between
base current and Vbe, an FET used as the amplifier that
has a quadratic Vgs to Idss relation or a thermistor used
for amplitude stabilisation. The latter is non-linear if the
resonant frequency is close to the thermal time constant but
linear if it is much higher since the thermistor is a pure
resistor at any given temperature. The result of non-linearity
is usually to produce harmonics, predominantly second for
the FET, third for the thermistor and lots for the transistor ;-)

I hope that clarifies what I mean and why I do not consider
it "indispensable" for resonance. In my work it is usually
undesirable except in frequency multipliers.

So when you are speaking of nonlinear transformer of energy and when
George Dishman speaks of linear RLC circuit, it would be interesting
to ask you for more precise thesis. Aren't you against?

I hope I have clarified my meaning, there are no higher
order terms in the transfer characteristics of resistors,
capacitors or inductors hence no harmonics produced.
Note though that a pendulum need not be a linear system
in my view since the restoring force is only proportional
to displacement as an approximation at low amplitudes.

[I wrote:]
Remember, a child on a swing is a resonant system, small
pushes correctly timed can build up a large amplitude,
but it is not a wave phenomenon.

May I ask you, what are the components of wave phenomenon? If a wave
propagates in water on which a child swims - this is a wave
phenomenon, but a child as a heterogeneity with which the wave
interacts - this is not a wave phenomenon? ;-) It seems, you are
suggesting too simplified approach.

The words "wave phenomenon" mean a phenomenon created by
waves. The interference patterns created when the waves reflect
from the child are a wave phenomenon but the child would still be
there if the waves were removed.

But if a child sits on a pneumatic dolphin either stands on a boat,
will it essentially change the pattern?

I would say the pattern is a wave phenomenon but the child is
only part of the system that is creating the pattern. The child is
not created by the waves.

Perhaps you would like to say,
if we think a child as an integral body, this will be not a parametric
excitation, but if as a system having its own resonance subsystems,
this will be a parametric excitation?

Possibly, which parameter do you think is being varied?

Possibly, but this is always a
very conventional issue that depends on relationship between the
natural frequencies and excitation frequency. ;-)

Parametric excitation from what I have read on the subject
means excitation by variation of one of the parameters of
the system rather than by applying a simple signal.

I would call a system where there are multiple resonant
frequencies, such as the child on the boat, "compound".

If you connect a motor to the plates of a capacitor to move
them closer or further apart and use that in an LC circuit,
it is "parametric" and the parameter being changed is the
capacitance. One important aspect is that the resonant
frequency is varied during each cycle in the parametric
case although this is not a definition nor perhaps even
necessary (if the parameter does not play a part in setting
the resonant frequency).

George