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Re: Sodaplay: Tacoma Narrows resonator



There is a semantic question here which may be worth elaborating. The
(small)motion of a complex system (eg. a stretched string) may be
mathematically analyzed into a compounding of "normal mode" oscillations
at its "natural" frequencies.
"Resonance" is a relation between such a system and an excitation
mechanism which itself oscillates in time at one of the system's natural
frequencies (or, more generally, when its frequency spectrum contains a
large component at such a frequency).

I would not apply this term ("resonance") to the natural oscillations
which result from an "amorphous" excitation - eg, a plucked or bowed
string. It is of course true that the exact manner of plucking /bowing
will determine the amount of excitation of each natural frequency, but
there is here no "resonance" between the spectrum of the system and the
spectrum of the excitation.

The marching soldiers phenomenon would be a resonance phenomenon - the
excitation is pulsed and can contain a large spectral component which
"resonates" with a system natural frequency.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

----- Original Message -----
From: "William Beaty" <billb@ESKIMO.COM>
To: <PHYS-L@lists.nau.edu>
Sent: Thursday, December 07, 2000 03:49 PM
Subject: Re: Sodaplay: Tacoma Narrows resonator


On Thu, 7 Dec 2000, Leigh Palmer wrote:

Sounds suspiciously like this is fostering a well known misconception.

You're right!

The Tacoma Narrows Bridge was not driven by an oscillatory wind; it
was an aeolian oscillation driven by a steady wind. I will guess that
the simulator demonstrates a resonance phenomenon. As I've pointed out
more than once, the Tacoma Narrows Bridge collapse is not an instance
of a resonance phenomenon.


Hmmm. "Resonance" seems to have two meanings: sympathetic vibrations,
versus vibration mode of a system. The bridge was a resonance
phenomenon
in that it break into oscillation at a resonant frequency. However,
since
the wind wasn't pulsing, it wasn't a sympathetic vibrations phenomenon.

I suppose the sodaplay simulation better illustrates the legendary
marching soldiers problem.



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