I think it is reasonable to add the simple/conical pendulum to the
misconception list as Ludwik suggests.
The explanation as written also seems okay, except I think the
dependence of period on the angle is stated backwards. It depends upon
the choice of theta. If theta is the angle between the pendulum string
and a vertical line, then the simple pendulum period increases with
theta whereas the conical pendulum period decreases with theta.
I believe this would be the standard definition of theta, and if
defined as such, the maximum theta is typically how one describes the
amplitude of the simple pendulum.
I agree with Ludwik that the conical pendulum does not have an
"amplitude" in the sense that amplitude typically means the maximum
deviation for an object oscillating through its equilibrium position;
and the conical pendulum rotates at constant deviation from the
equilibrium position rather than oscillating through it. But unless
someone can suggest a better name for the angle of the conical
pendulum, I am not opposed to calling it an amplitude.
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
-----Original Message-----
From: Ludwik Kowalski [SMTP:KowalskiL@MAIL.MONTCLAIR.EDU]
Sent: Friday, August 06, 1999 1:26 AM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: "Simple pendulum"
<snip>
And second, because it is not possible to have "the same
THETA and the same frequency" at large angles. The
conical pendulum and the simple pendulum do have nearly
identical periods at small angles (assuming L and g are
identical) but at large angles the dependence of T on angle
is different in each case. It turns out that for a simple
pendulum T decreases with THETA while for a conical
pendulum T increases with THETA.
<snip>