Experiment Analysis

Question 1

Show that the equation
    (9.4)
reduces to
    (9.2)
when and are small.

a. Expand in a Taylor series about x=0, retaining only its first two terms.
    (9.6)
The limit as x gets small is
    ( x small)

b. If = 0.02034 show that the second term in eqn. (9.6) is small relative to the first so that
    (9.7)

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.
    (9.8)
    (y small)

f. Rewrite the right hand side of eqn. (9.4) assuming and are small:
    (9.9)

g. Use and simplifying eqn. (9.9)
    (9.10)


We have now completed the loop by showing that eqn. (9.2) is the same as eqn. (9.4) when and are small.

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