Experiment Analysis
Question 1
Show that the equation
reduces to
when
and
are small.
a. Expand
in a Taylor series about
x=0, retaining only its first two terms.
The limit as
x gets small is
b. If = 0.02034 show that
the second term in eqn. (9.6) is small relative to the first so that
c. Calculate
for
s, the largest time
in Table 1.
d. Now calculate the maximum value of the argument
of the inverse hyperbolic tangent function in eqn. (9.4).
argument= 0.02034 + 0.03475 = 0.05779
e. Expand tanh
y in a Taylor series about
y=0 retaining only the first two terms of the series. Show that
the second term of the series is small relative to the first.
f. Rewrite the right hand side of eqn. (9.4)
assuming
and
are small:
g. Use
and
simplifying eqn. (9.9)
We have now completed the loop by showing that eqn. (9.2) is the same
as eqn. (9.4) when and
are
small.
Copyright
1998-1999
Rensselaer Polytechnic Institute. All Rights Reserved.