Numerical Integration
Exercise 2

The pend_plot.pdf shows the result. The approximate period is 1.42 s. The 
exact and approximate periods agree to within 1% up to an amplitude of 0.41
or about 24 degrees. The exact period is always longer than the approximate
period.

When the program is run it gives the following result
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In [7]: run exercise02
Warning: Extremely bad integrand behavior occurs at some points of the
  integration interval.
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The poor behavior is at amp = pi. Theoretically, at amp = pi, the pendulum
would be balanced above the pivot and would never oscillate, i.e., the 
period is infinite.
