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



At 09:00 PM 3/17/2007, you 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.

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.



Brian Whatcott Altus OK Eureka!


I see that I should have defined my use of amplitude as maximal
displacement on the horizontal axis, because it otherwise seems
to conflict with the usual math model that other esteemed
contributors are trotting out, which is couched in terms of angular
change.
I will say that in my view it is so intuitive to discuss
the idea that 1/2 mv^2 = mgh ignoring losses that it provides a
natural student springboard to other oscillator energy exchanges



Brian Whatcott Altus OK Eureka!