Re: [Phys-l] Queston: simple pendulum lengthen suspension.

[Bernard Cleyet <bernardcleyet@redshift.com>]

Brian Whatcott wrote:

> At 03:41 PM 3/17/2007, you wrote:
>
>  
>
> > What happens to the amplitude if one suddenly lengthens the suspension
> > at equilibrium position or at max. displacement?
> >
> > bc, puzzled
> >    
>
> Sticking to the idea of an oscillator, which constantly switches energy
>  between modes: in this case kinetic and potential energy: I see that
>   lengthening the pendulum at the center position, while holding its
> sidewards kinetic energy constant allows the pendulum's amplitude
> to increase, so that it gains the same potential energy as before at
> the end of stroke.
>  
U = mgh = mgl(1- cos A)

If l is longer, then A should be smaller???

what is my problem?

> If the pendulum's length is increased at the end of stroke, the
> ensuing exchange to kinetic energy involves a smaller transaction,
> because less potential energy is converted by the reduced drop,
> though the former amplitude is maintained.
>
> These model manipulations are simplified by considering that the
>  change of length is taken at the pivot.
>  
yes. (latter)

This case is intuitive, as long as the reduction in potential E by 
dropping the bob is not converted into bob KE, which seems the case;  
where it goes is not clear to me.

I modelled this numerically and obtained the BW result.  Curiously, (At 
least bc is curious.) The increase in amplitude is directly proportional 
to the period increase.

bc, still puzzled.


> Brian Whatcott    Altus OK    Eureka! 
>
>
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