[Phys-L] explanation(s) Was: Re: Typing Math Equations in Email - the Pendulum!

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2015, Apr 04, , at 19:50, brian whatcott <betwys1@sbcglobal.net> wrote:

> I enjoy reading of Bernard's experiments with a pendulum. It is, I suppose, unfair to quote phrases from a pdf on this topic which he offered simply to show a method of displaying equations.
>
> Still, I cannot suppose he would deliberately put up text that he would not support, so I am bold enough to say that several of his assertions appear (to me) to be self-contradictory. The ones in question,  I marked as 1) and 3)
>
> I also have a difficulty with item marked 2).
> I would like to paraphrase this as
> ..adding mass (to a pendulum) will reduce the amplitude at equilibrium for a given total or mean energy, and probably
> for a constant input energy for that matter.
>
> Numbered Excerpts from "Q in Mechanical Oscillators" (BC)
>
> 1) ... "the pendulum was stopped after each attainment of equilibrium and free decay, and an additional mass added. Note the amplitude decreased with increasing mass!"
>
> 2) ..."adding mass will not reduce the energy to maintain a given amplitude. "
>
> 3)..." I’ve shown experimentally, contrary to many’s intuition, that the mass of a pendulum’s bob does not significantly affect it’s driven equilibrium amplitude. "
>
>
> I feel sure that Bernard can explain the apparent contradictions....
>
> Brian Whatcott


For number three:  I shoulda writ doesn’t increase its equilib. amp.   This supposed increase is a common belief.  Probably because the majority experience is an increase in Q results in an amplitude increase, because the Q increase is due to a change in the resistance (electrical) or drag (e.g. dashpot mechanical oscillator).  Instead, as I wrote, it decreases due to support movement.  Tho the lab bench (coffee table) to which the rotary motion sensor is clamped is massive (~ 100#),  the sensor itself is not, and its case if made of rather compliant plastic.  An extremely rigid and massive support will, of course, render the decrease imperceptible.  

#2 is a simple conservation of E statement except of course the increased loss due to support movement increases the E necessary to maintain amplitude.  

Support movement was well recognized more than a century ago, e.g.  the support here:  


http://www.bmumford.com/mset/courthouse/


The same escapement as here:  (note massively supported)

1859:   http://www.parliament.uk/about/living-heritage/building/palace/big-ben/inside-clock-tower/how-great-clock-works/ 

Dawson the inventor of the three leg not given credit, just as Mitchell often not for the gravity torsion pendulum.  


https://books.google.com/books?id=9eMkgfKIdXIC&pg=PA294&lpg=PA294&dq=reverend+john+mitchell+weighing+the+earth&source=bl&ots=w_fvTEAV_z&sig=ge0-mkk7KGl4x_CzjzDS9WKkCY4&hl=en&sa=X&ei=-ZIhVe_0I9D3oATmpIHYCA&ved=0CCYQ6AEwAQ#v=onepage&q=reverend%20john%20mitchell%20weighing%20the%20earth&f=false  

bc