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Re: [Phys-l] What comes first, the equation or the explanation?



For what it’s worth, here are two casual observations:
1) If one does the experiment of changing the mass, he must simultaneously
change the driving frequency, since the resonant frequency is mass
dependent.
2) It may be worth noting from equation 4 that if “omega sub zero” is used
as the “resonant” driving frequency, then the amplitude B is independent of
mass.

From: Bernard Cleyet
Sent: Friday, December 23, 2011 6:52 PM
To: Forum for Physics Educators
Cc: Nancy Seese
Subject: Re: [Phys-l] What comes first, the equation or the explanation?

On 2011, Dec 22, , at 19:10, carmelo@pacific.net.sg wrote:

Perhaps, Feynman has answered Peter's question?

Omni: Do physicists vary greatly in their ability to see the
qualitative consequences of an equation?

Feynman: Oh, yes — but nobody is very good at it. Dirac said that to
understand a physical problem means to be able to see the answer
without solving equations. Maybe he exaggerated; maybe solving
equations is experience you need to gain understanding — but until you
do understand, you’re just solving equations.

alphonsus


Here's a problem wherein the equation predicts an effect, which I cannot
apprehend. If anything it's counter intuitive.

I've posted before the link to the derivation.

http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/Bob's%20mass%20affects%20driven%20pendulum's%20amplitude_/Amplitude(bob%20mass).1.key.pdf

Why does increasing the mass of a harmonically driven, with linear
dissipation at resonance, pendulum's bob reduce the pendulum's amplitude? I
haven't found any report of the experiment and only one source** wherein the
resonant frequency has been substituted in to the particular solution.
(fortunately, after I had the exercise of doing it.)

bc only just solved the equation.



** Modern analytic Mechanics, Cooper and Pellegrini (1999) p.27


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