Re: [Phys-l] Mass and SHO amplitude Was: Re: Student Misconceptions

[Bernard Cleyet <bernardcleyet@redshift.com>]

On 2011, Oct 07, , at 06:21, Philip Keller wrote:

>  But all of this seems kind of basic to me, which makes me suspect that I am completely missing the point of your question.  Can you tell what context motivates this?  And again, what mechanism increases the mass?


See my responses today.


The context is, for centuries horologists have known adding mass doesn't increase a clock's (usual pendulum clock, what ever the escapement including recently E-M drive) pendulum amplitude.

However, I found, If I'm not too maths challenged, that the amplitude decreases when mass is added.  The usual assumptions apply: support absolutely rigid and any other dissipation not changed, linear regime (small angle), and dissipation linear.  Also the drive is amplitude independent.  Incidentally I don't know of any escapement whose drive is independent of the amplitude.  I think an E-M drive may be made independent, but this requires a very accurate measure of the amplitude.


No sophisticated mechanism -- theoretical, however, if desired experimentally, replace the bob w/ an identical one except a different SG (specific mass).  Note, the support is not rigid the amplitude will change due to the loss change in the support.  also if the rod is not "massless" the period will change possibly complicating matters.  And there's the problem of changes in the suspension, for example both the rod and suspension will experience length change and the suspension, if a spring (most very accurate clocks use a spring), the point of rotation will change.  [Possibly not for the Fedchenko isochronous suspension.]


bc surprised, evidently, no one caught the question was about constant drive as with a clock.