In the beginning, I thought I might be able to imagine two reference
frames, one in which a simple pendulum looks like a simple pendulum,
and the other in which it looks like a conical pendulum, or vice-versa.
But upon more thinking, sketching, visualizing, etc. I am unable to
imagine this. In the meantime my mathematical and experimental
analyses have shown these are different physical systems, and I do not
believe it is possible to find the reference frames mentioned above.
For example, if the amplitude dependence of a simple pendulum is an
increasing period with increasing angle, and the amplitude dependence
of a conical pendulum is a decreasing period with increasing angle, I
don't see how any choice of reference frame could make these congruent.
But beyond that, I can't even picture the frames that would make one
look like the other. Let's start with a simple pendulum swinging as a
simple pendulum in my physics lab. Can anyone describe what frame I
would have to be in such that I would view this as a conical pendulum?
I assume it would have to be a rotating frame, but I cannot imagine
any axis of rotation, nor where I would locate myself in that frame,
such that this simple pendulum would appear conical.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817