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Unformatted text preview: pathologies. If your plot has little gaps in it, it’s because
MMA is generating tiny imaginary terms added to the result. You might just try plotting the real part
of the integral, using the command Re[ ]. Similarly, if it gives you symbolic results, you might ﬁx that
by using the command N[ ], which forces MMA to evaluate the expression as a number, if it can! By
the way, this integral is called the “complete elliptic integral of the ﬁrst kind”.
(c) A real grandfather clock has a length of about half a meter, and you pull the pendulum, oh, about 10
cm to the side. When designing the clock for practical use, would the clockmaker be safe in making the
“small angle” approximation? (What we mean here is to justify your answer with a calculation that
tells you whether this clock would be annoying or useful to have in your house! Can you be concrete
about what you would consider “annoying” about a clock?)
5. Two large solid spheres, each with mass M, are ﬁxed in place a distance 2l apart, as shown. A small ball of
mass m is constr...
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