Randall,

I haven't ever considered such a device and it sounds interesting.  Without
attempting to mathematically model it (which for me generally results in a
learning  process but very little usable results) I wonder what the effect
of the trapped and compressible air column is?  What would be the difference
in response if the air was isolated from the water or mineral oil by a
sealed partition in the tube so that it would not compress?  The tube would
be perforated below the partition to avoid trapping any additional air.

Also, I think it will be a challenge to restrain the tube so that it moves
vertically without adding friction or otherwise changing the response.  What
about one of your capacitance sensors set up so that it will only respond to
vertical motion?

I'm still studying your pendulum paper that posted a link to here some time
ago.

Regards,

Bob

On Tue, Dec 9, 2008 at 12:50 AM, Randall Peters wrote:

> I've been contemplating an instrument based on a piece of equipment we
> use in the physics department to teach hydrostatics.  It is a long tube
> that is sealed on one end, and the open end is immersed in a larger tube
> filled with water.  The smaller tube achieves an equilibrium position
> determined by its weight, overall length, and diameter of the internal
> air column.  If one lifts the inner tube and releases it, it oscillates
> in simple harmonic motion with a period greater than one second.  Also,
> because of the water, the motion is dampened.  The motion depends on the
> compressibility of the trapped air.
>    I've done an idealized calculation in which the water would be
> replaced with mineral oil and the plastic tube of the apparatus with a
> thinwall metal tube of length in the neighborhood of one meter.  It
> appears that the damping would be close to optimal and the period just
> under two seconds for the diameter of the inner tube being one
> centimeter and that of the outer tube holding the mineral oil about two
> cm's.
>    The inner tube should be constrained (perhaps with long triaxial
> threads, so that the motion is strictly vertical.
> I will be interested to know if any of you have considered such an
> apparatus.
>      Randall
>
Randall,

I haven't ever considered such a device and it sounds interesting.  Without attempting to mathematically model it (which for me generally results in a  learning  process but very little usable results) I wonder what the effect of the trapped and compressible air column is?  What would be the difference in response if the air was isolated from the water or mineral oil by a sealed partition in the tube so that it would not compress?  The tube would be perforated below the partition to avoid trapping any additional air.


Also, I think it will be a challenge to restrain the tube so that it moves vertically without adding friction or otherwise changing the response.  What about one of your capacitance sensors set up so that it will only respond to vertical motion?


I'm still studying your pendulum paper that posted a link to here some time ago.

Regards,

Bob

On Tue, Dec 9, 2008 at 12:50 AM, Randall Peters <PETERS_RD@..........> wrote:

I've been contemplating an instrument based on a piece of equipment we

use in the physics department to teach hydrostatics.  It is a long tube

that is sealed on one end, and the open end is immersed in a larger tube

filled with water.  The smaller tube achieves an equilibrium position

determined by its weight, overall length, and diameter of the internal

air column.  If one lifts the inner tube and releases it, it oscillates

in simple harmonic motion with a period greater than one second.  Also,

because of the water, the motion is dampened.  The motion depends on the

compressibility of the trapped air.

    I've done an idealized calculation in which the water would be

replaced with mineral oil and the plastic tube of the apparatus with a

thinwall metal tube of length in the neighborhood of one meter.  It

appears that the damping would be close to optimal and the period just

under two seconds for the diameter of the inner tube being one

centimeter and that of the outer tube holding the mineral oil about two

cm's.

    The inner tube should be constrained (perhaps with long triaxial

threads, so that the motion is strictly vertical.

I will be interested to know if any of you have considered such an

apparatus.

     Randall