Audio output is a tone similar to a struck metal bar, using a physical model developed from solving the partial differential equation.

You need a certain amount of mathematical background to understand
partial differential equations. It would be difficult to solve them
without a college-level course in the subject.

On the other hand, once the solution is known, a programmer can
implement a DSP algorithm based on the solution without needing to
understand how to solve differential equations. I don't know
differential equations myself, but I have implemented solutions in
this way a few times. This is possible because the solution to the
differential equation can be implemented, in many cases, as a finite
difference equation which is just simple algebra.

Also, if you have access to a symbolic mathematics program such as
Mathematica, it may sometimes be possible for someone familiar with
algebra but not with differential equations to set up equations to be
solved by the program. But it would be difficult to set up the
equations unless one had some sort of understanding of the terms, so
this kind of solution would normally be possible only in some cases or
for varying a prototype equation.

The Wikipedia has generally fairly accurate articles on mathematical
topics, but I couldn't recommend them for beginners, they are usually
rather terse summaries for people who already have a mathematical
background.

All this said, see Julius O. Smith's web pages or Perry R. Cook's
books and code (in the Synthesis Toolkit in C++) for how this sort of
thing is actually done. Some advanced differential equation models of
sounding objects have been done as Csound opcodes based on the work of
Smith's student Stefan Bilbao, also, e.g. prepiano (see his page
http://www2.ph.ed.ac.uk/~sbilbao/nsstop.html).

Hope this helps,
Mike

On Tue, Feb 21, 2012 at 3:01 PM, Stefan Thomas
 wrote:
> Dear community,
> I've read in the manual about the barmodel-opcode:
>>
>> Audio output is a tone similar to a struck metal bar, using a physical
>> model developed from solving the partial differential equation.
>
> I would like know: of which kind are these differential equations? Is it
> possible (for a person who isn't a mathematician) to solve these equations?
> I would like to use the solution for additive synthesis, if possible



-- 
Michael Gogins
Irreducible Productions
http://www.michael-gogins.com
Michael dot Gogins at gmail dot com