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Re: Coupled Pendulums

The behavior of the system is always describable as a superposition of the
two normal modes of oscillation. In one mode the two pendula oscillate
synchronously; in the other mode they oscillate anti-synchronously. How
much of each mode occurs depends on the starting conditions - thereafter
each mode conserves its own energy (the individual oscillators exchange
energy - the normal modes do not). (I speak of an undamped system.)
The behavior described in the post is only one possible motion and
necessitates the excitation of both normal modes. Consult intermediate
mechanics texts (eg Barger and Olsson) for detailed analysis of such
coupled oscillator systems. Even if the mathematical treatment is beyond
an intro class, once the subject is broached then the "pure single mode
behavior" should perhaps also be experimentally demonstrated.

Bob Sciamanda
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor
----- Original Message -----
From: "Joe Taylor" <jtaylor@HAL.BSCS.ORG>
To: <PHYS-L@lists.nau.edu>
Sent: Monday, September 24, 2001 11:30 AM
Subject: Coupled Pendulums


Hello Phys-L gang,

I was wondering if anyone would mind sharing their explanation of
the
motion of a coupled pendulum (two or more pendulums suspended from
a
horizontal section of string.

I set the first pendulum to oscillate and left the second at rest.
Here
is what I seem to be observing when both pendulums are the same
length...

1) The first pendulum begins to oscillate (of course)
2) Shortly after the first, the second pendulum begins to
oscillate as
well .
3) The two oscillate together for a time and then the first comes
nearly
to rest. When the first comes to rest, the amplitude of the second
seems
to be near its maximum.
4) The first will begin oscillating again while the second comes
to
rest. Again, the first seems to reach a maximum amplitude when the

second returns to rest.
. . .
Joe Taylor