In this paper, Newton's equations are solved to describe the motion of a conical pendulum in a rotating frame for the right- and left-hand conical oscillations. If the pendulum is started with the initial angular velocity (±ω0Ωz), withω0 being the frequency of pendulum oscillation and Ωz the angular velocity of the rotating frame around the z-axis, the paths are shown to be circular, which would apparently indicate that the Coriolis force becomes non-effective in the rotating frame. This paper explains why the paths in the rotating frame are circular, and the difference between the periods for the right- and left-handed rotations is calculated analytically. It is also shown that in an inertial frame, the conical pendulum follows an elliptical path. As the Bravais pendulum is a conical pendulum oscillating at Earth's surface, its motion is also discussed.

1.
L.
Foucault
, “
Démonstration physique du mouvement de rotation de la Terre au moyen du pendule
,”
C. R. Acad. Sci.
32
,
135
138
(
1851
), see https://gallica.bnf.fr/ark:/12148/bpt6k2989j/f135.
2.
M. A.
Bravais
, “
Sur l'influence qu'exerce la rotation de la Terre sur le mouvement d'un pendule à oscillations coniques
,”
C. R. Acad. Sci.
33
,
195
197
(
1851
), see https://gallica.bnf.fr/ark:/12148/bpt6k29901/f197.image.r=bravais?rk=64378;0.
3.
M. A.
Bravais
, “
Mémoire sur l'influence qu'exerce la rotation de la Terre sur le mouvement d'un pendule à oscillations coniques
,”
J. Math. Pures Appl. Sér.
19
,
1
50
(
1854
), see https://archive.org/details/s1journaldemat19liou/page/n13.
4.
R.
Moekel
, “
The Foucault pendulum (with a twist)
,”
J. Appl. Dyn. Syst.
14
(
3
),
1644
1662
(
2014
).
5.
J.-P.
Pérez
and
O.
Pujol
, “
Two often disregarded aspects of Foucault's pendulum
,”
Eur. J. Phys.
36
,
015019
(
2015
).
6.
R.
Verreault
, “
The anisosphere as new tool for interpreting Foucault pendulum experiments. Part I: Harmonic oscillators
,”
Eur. Phys. J. Appl. Phys.
79
,
31001
(
2017
).
7.
D. B.
Plewes
, “
Magnetic monitoring of a small Foucault pendulum
,”
Rev. Sci. Instrum.
89
,
065112
(
2018
).
8.
M.
Beech
,
The Pendulum Paradigm: Variations on a Theme and the Measure of Heaven and Earth
(
BrownWalker Press
,
CA
,
2014
), p.
200
.
9.
W. F.
Rigge
, “
Experimental proofs of the Earths's rotation
,”
Pop. Astron.
21
,
208
216
(
1913
), see http://articles.adsabs.harvard.edu/full/1913PA.....21..208R/0000208.000.html;
W. F.
Rigge
,
Pop. Astron.
21
,
267
276
(
1913
), see http://articles.adsabs.harvard.edu/full/seri/PA.../0021//0000267.000.html.
10.
V. M.
Babović
and
S.
Mekić
, “
The Bravais pendulum: The distinct charm of an almost forgotten experiment
,”
Eur. J. Phys.
32
,
1077
1086
(
2011
).
11.
G.
Barenboim
and
J. A.
Oteo
, “
One pendulum to run them all
,”
Eur. J. Phys.
34
,
1049
1065
(
2013
).
12.
W. S.
Kimball
, “
The Foucault pendulum star path and the n-leaved rose
,”
Am. J. Phys.
13
(
5
),
271
277
(
1945
).
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.