RE: Forced damped pendulum

["Quist, Oren Phys" <QuistO@mg.sdstate.edu>]

I agree.

But, it is my opinion (humble though it may be) that it is the normal   
solution to the standard differential equation that best leads to an   
intuitive understanding of the significance of the various terms --   
damping, driving force, driving frequency, or whatever.  Numerical   
techniques can yield interesting answers, but much of the intuitive   
connections get lost in the details.
Oren Quist

 ----------
From:  Sam Held
Sent:  Tuesday, June 09, 1998 12:45 PM
To:  QuistO; RAUBERJ; phys-l
Subject:  RE: Forced damped pendulum


Oren,
 After giving this problem thought, I noticed no one corrected me
that we cannot use Lagrangians here due to the damping term.  I guess I
wsn't the only one without the morning coffee before answering e-mail.
However, learning simple nonlinear diff eq. methods like phase plots
should not be hard.  One can even lessen the learning curve by first
teaching the regular pendulum, then damped (or dirven), and finally   
driven
(or damped).  Then most numerical method books will tell you how to
numerically solve ODEs (Ordinary Differential Equations) and some do
PDEs (Partial Differential Equations).  Learning some about a computing
language (like C++ for example) would be good to put on the old college
application.


       Sam Held

sheld@utk.edu



On Mon, 8 Jun 1998, Quist, Oren               Phys wrote:

> I suspect that worrying about types of damping, non-linear terms, and   
    

> using Lagrangians is way off base for this high school student.  I   
think
> referencing a source on solving the normal DSHM equations would be
> sufficient.
>
> I would recommend:
>
>  MECHANICS, by Symon, Addison Wesley, 1960 (also 1971), p 47 +
>
> or a book by Becker -- I can't find mine -- who borrowed it??
>
> or I suspect most classical mechanics books (Marion?) etc. will handle
>  the solution particulars of the resulting DSHM differential equation.
>
> I hope this helps.
> Oren Quist, SDSU

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