Re: [Phys-l] Another practical problem

[brian whatcott <betwys1@sbcglobal.net>]

On 2/15/2011 1:00 AM, Bernard Cleyet wrote:
> I've posted my question about the effect on the amplitude from adding mass to a pendulum bob.  I didn't receive a useful reply, so I made an app. that conversely drops a mass from the bob of a pendulum at ~ any desired time.  I haven't though of a method that adds mass w/o "disturbing" the P. other than just adding mass.
>
> Pics of the app. are here:
>
> Index of /Horological/weight pan effect/Magnetic drop
>
>
> I've collected data for one trial; dropping the mass very soon after passing BDC on its upward swing.  The RMS gives position data from which one may also plot the angular speed of the P.
>
>    Care to predict the result?  Which I'll post after fitting:  Angle = A (exp(-C0*t))(sin(2Pi *f * t + C1)) + C2, I pray.
>
> bc
Ho hum... a thought experiment:-   machine three bobs as right cylinders of
 constant diameter:  one of aluminum, one of lead: both these of the
same mass: and a third bob, this one of the same diameter and volume
 as the aluminum  one, but made of lead.

Now consider the Q factor of an oscillating device, but THIS time, rather
 than introducing the idea  of electrical/mechanical analogs, to 
justify the
 means by which Q is increased, consider a more general definition for Q:
it is  the ratio of energy stored per cycle
 divided by the amount of energy dissipated per cycle.

It is known that  for constant energy input per  cycle, a  device
oscillating with higher Q gains greater amplitude. Similarly,
if it oscillates freely, it will vibrate longer if its Q is higher.

We can say that similar pendulums swinging on a light suspension with
 an effective pivot  will dissipate some energy to air drag. I described
above a means of providing three isochronous  pendulums, given
 that they can share the same effective length.

To avoid issues of adding or subtracting mass on the fly, we can imagine
 each  of the three being released from constant displacement by a thread
touched with a flame in the traditional way: or possibly a thin wire fuse
 blown electrically.

Consider the  pendulums of constant mass.  The lead bob being denser offers
 less cross section for drag, and so we can confidently suppose that it 
will show
 the higher Q, that is to say, it will vibrate longer than the aluminum one
 before coming to rest.

Finally, consider the pendulums of constant volume: the lead one being 
about
four times heavier falls with more acceleration than the aluminum one, for
almost the same reason a balsa wood ball falls slower from the Tower of 
Pisa,
compared with an iron cannon ball of the same diameter.
 (Galileo notwithstanding)

Conclusion: if your experiment did not confirm that shedding bobweight
 reduces Q and hence reduces steady state  amplitude for constant 
energy input,
you did not control enough factors    :-)

Brian W