
The pendulum rod is assumed to be of negligible mass as is the drag force on the bob when
exposed to air.
The bob is subject to a gravitational force W at all times along with a drag force F
D
and buoyant
force F
B
acting on it while it is submerged. The forces are shown in Figure 6.54 for both cases.
The pendulum dynamics are modeled by the different ial equation
J
d
2
u
dt
2
¼
(W þ F
B
)R sin u F
D
R, u
L
u u
L
WR sin u, juj > u
L
(6:305)
Expressions for the constant buoyant force and assumed linear drag force are
F
B
¼ gV ¼ E
4
3
pr
3
(6:306)
F
D
¼ av ¼ aR
du
dt
(6:307)
where
g is the specific weight of the liquid
V is the volume of the bob
a is the drag coef ficient
Combining ...