On Wed, 27 Oct 2004, Denny Esterline wrote:

>> Why don't you simply build a simple pendulum with period ~1 second (~1
>> meter long) put it in a thermostated pipe and measure its period. It would
>> have an oscillation amplitude of ~5mm (throw = 10mm) and you need to
>> detect it to 1/1000 (10um) precision using the microscope over say 100
>> seconds (periods). That is 1 part in 100,000. So you kick the pendulum
>> perhaps using a small electromagnet and then you watch the first pass and
>> count time till the 100th. A heavy pendulum with such a small amplitude
>> should give you much longer than 100 seconds time between 'kicks'. I
>> suggest you suspend the pendulum on a steel wire (guitar string etc)
>> instead of using a bearing. Some old clock pendulums used this method of
>> suspension.

^^^^ Oops = the period of a 1 meter long mathematical pendulum is not 1 
second. The Formula is T= 2*PI*sqrt(l/g) and the correct time for 1 meter 
is 2 seconds (nominal).

>> Peter
>
> There's actually quite a few 'details' glossed over by that scenario.
> First, the pendulums' period *does* depend on it's amplitude - not a
> lot, but way more than the tolerances in this project. But it can be
> compensated for, a couple of slot pairs for timing and amplitude
> sensing and a electromagnet to give it a kick.

I am pretty sure that the pendulum will have a repeatable time over 100 
periods even if the amplitude changes (decays) if the initial amplitude 
(kick) is constant to the nearest 10um. This can be achieved with feedback 
control from the microscope. This is not to be an absolute instrument. You 
do not want to tamper with the pendulum while it is being timed. You want 
to stop it (probably using an electromagnetic brake), then kick it with a 
defined amount of current for a defined amount of time, and then measure 
without further touching it. The magnetisation is a good point but a 
copper ring + ac powered magnet could be used to avoid this. Obviously the 
details are glossed over, this is a concept.

> Second (and most relevant) is the precision needed in the reference
> oscillator. To produce meaningful results the reference osc needs to
> have a very small drift - on the order of 10^-9 per day or better.
> This should be achievable with an OCXO, but GPS disciplined would be
> better (now to find a way to do it on my budget :o)

How much sensitivity do you need ? To measure 1x10^-5 you need 2x10^-6 
clock stability for the measuring period with a pendulum. That's why they 
stopped using pendulums for this I think.

> As to the suspension system, the best ones I've read about are
> "Kater's pendulums" (sp?) they were the first devices to establish 'g'
> to about four decimal places. They use a knife edge against a glass
> substrate.

The flexure suspension is more accurate after it ages and settles. The 
Kater pendulum had to be inverted for use and was timed manually afaik. 
The Boys, Cavendish-Hill Coulomb etc systems used torsion wires as 
suspension. The torsion wire suspension is a type of flexure suspension. 
The Askani (sp?) gravimeter uses a horizontal spring to suspend the mass 
at the end of a lever. This is also flexure.

Peter
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