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Re: [Phys-L] a counterintuition: please examine



Any math model that did NOT show decreased pendular amplitude for increased bob weight would be in error. You are attributing decreased amplitude to decreased Q instead of the usual interchange of kinetic and potential energy with constant impulse energy. Putting that aside, you said that clockmakers note decreased Q with increased bob weight and that is the question of interest! I take that to mean the time for ampliitude to fall to a fraction of its initial value of course.
On Saturday, August 7, 2021, 02:43:26 PM CDT, bernard cleyet <bernard@cleyet.org> wrote:



On 2021/Jul/18, at 08:28, Brian Whatcott <betwys1@sbcglobal.net> wrote:

...but wait a moment; if a constant energy input per beat is provided, like bc describes, WHY is Q reduced as shown by reduced amplitude?The factors in play are air drag and pivot friction, so it is plausible to suggest that increased mass increases air-drag cross-section and/or total surface area of the bob, and increased weight increases pivot friction.


Nope, IIUC, nothing changes except the increased mass.  Look at the ODE. 


An experimental arrangement where mass is added to an internal bob cavity or the pendulum is situated in an evacuated tube, and where the slope of pivot friction versus weight is reduced by providing an air bearing or possibly a magnetically floated pivot point - might well shed light on this.
About pivot friction, it is well known that rolling friction tends to be less than sliding friction, so that a stiffly supported pin roller bob, pivoting on a stiff hard plane mount might well provide a higher quality factor Q. This method would have been accessible to clock makers for hundreds of years, so I expect it has more deficits than the fragility to bumps that is easy to imagine.
    On Sunday, July 18, 2021, 09:36:32 AM CDT, Brian Whatcott <betwys1@sbcglobal.net> wrote: 

BC's elucidation of his conditions for finding that increased mass reduces pendular amplitude reveals that he did in fact add mass at the location where bob velocity would be greatest, as Bob and I surmised.
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