Natural Science Forum / Physics / Acoustics / October 2004

Hi ypj,

   i think your question is like this:  "if i put 10 points of energy
in, how in the heck can i get 100 points out?"

   good question.  resonance is a phenomenon caused by stored energy.
imagine a pendulum ball on a string.  if you push it once, it
continues to swing back and forth for a while...

   a child on a playground swing is a resonant phenomenon.  push the
swing once, and it goes so hi.  push it again, and it goes higher...
continue to push in time with the swings motion and you drive the
swing higher and higher and higher...  the reason that it goes higher
and higher is that alot of the kinetic energy you put into the swing
with the first push is still present when you push for the second
time.

   if all the energy came out before you pushed a second time, the
swing would be sitting still again when you pushed that second time,
and the amplitude of oscilation would not increase with additional
pushes.

   resonance is fascinating, and discussion of it usually comes with
disucssion of damping.  damping is the rate at which energy is taken
out of the system.  (imagine you were pushing the same swing, but
instead of through air, it moved through maple syrup, it would slow
down very quickly).

   an so in any case, the oscilations of any real world systemwill
not build indefinitely, but will build until energy in = energy out.
energy in is the driving force, energy out is damping in all of it's
various forms.

   and so it follows that more damping = lower oscilation at a
resonance frequency for any system, all other variables equal.

   i hope my comments are helpful - the answer you seek is this:  the
oscilations can build and build because energy is stored.

    is it possible to post pictures in this forum?  i could show this
visually and make much more sense out of it.

Brian

Hi ypj,

   i think your question is like this:  "if i put 10 points of energy
in, how in the heck can i get 100 points out?"

   good question.  resonance is a phenomenon caused by stored energy.
imagine a pendulum ball on a string.  if you push it once, it
continues to swing back and forth for a while...

   a child on a playground swing is a resonant phenomenon.  push the
swing once, and it goes so hi.  push it again, and it goes higher...
continue to push in time with the swings motion and you drive the
swing higher and higher and higher...  the reason that it goes higher
and higher is that alot of the kinetic energy you put into the swing
with the first push is still present when you push for the second
time.

   if all the energy came out before you pushed a second time, the
swing would be sitting still again when you pushed that second time,
and the amplitude of oscilation would not increase with additional
pushes.

   resonance is fascinating, and discussion of it usually comes with
disucssion of damping.  damping is the rate at which energy is taken
out of the system.  (imagine you were pushing the same swing, but
instead of through air, it moved through maple syrup, it would slow
down very quickly).

   an so in any case, the oscilations of any real world systemwill
not build indefinitely, but will build until energy in = energy out.
energy in is the driving force, energy out is damping in all of it's
various forms.

   and so it follows that more damping = lower oscilation at a
resonance frequency for any system, all other variables equal.

   i hope my comments are helpful - the answer you seek is this:  the
oscilations can build and build because energy is stored.

    is it possible to post pictures in this forum?  i could show this
visually and make much more sense out of it.

Brian

(sorry if this is a double-up, i'm struggling to figure out how to
post in this forum)

yes.

Yes; STORED in the vibrating system. We must distinguish between energy
and power (the FLOW of energy).

As long as the dissipation of energy in the storage system is less than
the flow of energy (power input), the amplitude of the oscillations will
increase.

    Energy is taken from the environment in general. Good example is the
conch shell, where some environmental noise is captured in a partly
closed, partly open cavity; and where the amplitude within increases
until the sound absorption matches the coupled input acoustical power.
Someone here measure one instance of amplitude buildup at 10 to 15 dB
"amplification"(?).

    Energy is lost via  friction in the system, which increases, usually,
for vibration, as the square of the instantaneous speed, but in general
it could have any schedule, and could be linear or nonlinear (snubbed,
damped, catastrophic... anything goes).

    Angelo campanella