Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] checking the work for minus signs ... et cetera


On 2015, May 15, , at 12:06, brian whatcott <betwys1@sbcglobal.net> wrote:

Bernard,

I replicated your value for Q given the following assumptions which I presume you made:
1) the effective pendulum length l is obtainable from Period = 2.Pi. root(l/g)

yes


2) The value for g at Trinity is 9.8 N/kg.

yes, however in my method it “cancels”. [except for the length, which changes little (0.2%) as the change is ~ delta (g)/2 ]

The pendulum amplitude is 55mr.
3) The maximal value for pendulum energy occurs at the potential energy max.

? is ~ constant, and I understand your reasoning, which I used. BTW, there’s a web site that gives the E for M, g, A,and T; and the speed at BDC!


4) Infinitely rigid (support), lossless pivot

Not necessary as the drive “cancels” all the dissipations.


If I choose instead the moment where angular displacement = 0 mr
and an escapement increment has occurred, the maximal KINETIC energy is calculated by adding half the escapement energy to the peak potential energy (the other half of the escapement's energy contribution being dissipated as the bob returns to a 0 angular displacement.) This changes the value for Q but only slightly.
Similarly, the amplitude of this clock varies: today (friday) it is 47 mr which has a much more distinct effect on the value of Q obtained.


Yes, only v. ~ 17% high now.


I assume the Q was measured as a decay over “some” time with the pendulum moving the gravity arms only, which is likely a problem. This is because I only know of two persons(1) who've used the “bc” continuous Q measurement method, which finds the Q at the running amplitude instead of an average.



Moreover, in the Cambridge vicinity, g runs 9.81
See http://www.bgs.ac.uk/products/geophysics/landGravity.html for N52.33 W0.0

None of this explains the large difference between your value and that provided for Dr Hunt.
I notice that no estimation of the effect of suspension pivot rigidity in space is given, other that a speculation about wind-driven deflection of the tower.

Brian W
[I see that Doug S Drumheller - Sandia emeritus and Hugh Hunt at Cambridge are both on your copy list. It would be interesting if they care to contribute.]


(1) Drumheller, Douglas Measuring Amplitude, Velocity, and Q HSN 2012-4 The author describes an improved version of the "bc" method w/ an example.
And B. Mumford who has incorporated it in one of his software versions accompanying the MicroSet.

On 5/14/2015 4:28 PM, Bernard Cleyet wrote:
/snip/ The Cambridge Clock (Trinity College) has been examined in detail in order to ascertain if it can detect the g variation due to the moon. (1)
My interest is in its running Q. The escapement supplies energy (to the pendulum) from the drop of the gravity arm; mass 50 g thru 3mm every 1.5 seconds. (three second period)
The bob's mass is 104 kg (calculated from other data, i.e. not measured directly), and the running amplitude is 55mrad.
/snip/
The alternate is to separately find the pendulum’s energy and divide it by the escapement energy.
This is a method described by Woodward (2) in, IIRC, "My Own Right Time” to find the running Q.
/snip/
p.s. Assumptions and approximations include: zero rod mass and bob a point. And I did not obtain the published value from the keeper of the clock reported by Drumheller. (3) (bc=> 7358 Dr. Hunt, fellow Trinity College: 4570)

(1) Lupton, R. The Trinity Clock
http://trin-hosts.trin.cam.ac.uk/clock/?menu_option=theory

(2) Philip Woodward - Wikipedia, the free encyclopedia http://en.wikipedia.org/wiki/Philip_Woodward

(3) Drumheller, Douglas S.; Barometric compensation of pendulum JAM-11-1236 (copy supplied by the author. The shorter article in the HSN doesn’t include this information.)


cut