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



The problem is much simpler if you just think "differental equations".
At any instant of time you are allowed to constants to determine the behavior of the undisturbed system for all subsequent times. So the physical question is limited to: How does the lengthening process affect the angle, and how does it affect the velocity of the bob.
Regards,
Jack



On Sat, 17 Mar 2007, Bernard Cleyet wrote:



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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_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l


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