
362 Classical Mechanics
The physical force acting on the bob is the vector sum of the tension
in the cord and the weight
of the bob
. If we neglect the centrifugal force term, then
eff
, and the equation of motion
of the pendulum bob is
m
r
mg Tm v
δ
ω
2
2
2
′
=+
. (11.65)
It is clear from Figure 11.19 that the components of
are
T
b
/T = b/l or T
b
= bT/l
T
x
= −xT
b
/b = −xT/l, T
y
= −yT
b
/b = −yT/l, T
z
= (l − z)T/l. (11.66)
Equation 11.65 then reduces to
mx
x
l
Tmzy
my
y
l
Tm
′
=−
′
−
′
−
′
′
=−
′
−
2
2
ωλ λ
ω
(cos sin)
′
′
=
−
−+
′
x
mz
lz
l
Tmgmx
sin
cos
λ
2
. (11.67)
A fourth equation that relates x′, y′, and z′ is provided by the constraint equat ...