48
CHAPTER 2. DIMENSIONAL ANALYSIS
to form the expression
or
It is interesting to note that the mass of the pendulum apparently is unimportant because it doesn’t appear in either of the dimensionless terms. Because length
and time have non-zero exponents, the motion of a simple pendulum is a kinematic
physical process.
Exact Solution. The governing second order ordinary differential equation for the
simple pendulum in the absence of air resistance is given by
which has an exact solution (Beer and Johnson 1962)
T = 2 K\
where K(0m) is the elliptic integral
■6,
tf(M = /
Jo
do
Beer and Johnson (1962) reported that the function
varied from 1.002 rr
at 6m = 10° to 1.073 it at 6m = 60°. Thus, the motion of a simple pendulum is
only weakly dependent on the angle of release.
CHAPTER 2. DIMENSIONAL ANALYSIS
to form the expression
or
It is interesting to note that the mass of the pendulum apparently is unimportant because it doesn’t appear in either of the dimensionless terms. Because length
and time have non-zero exponents, the motion of a simple pendulum is a kinematic
physical process.
Exact Solution. The governing second order ordinary differential equation for the
simple pendulum in the absence of air resistance is given by
which has an exact solution (Beer and Johnson 1962)
T = 2 K\
where K(0m) is the elliptic integral
■6,
tf(M = /
Jo
do
Beer and Johnson (1962) reported that the function
varied from 1.002 rr
at 6m = 10° to 1.073 it at 6m = 60°. Thus, the motion of a simple pendulum is
only weakly dependent on the angle of release.