IODE PROJECT 3

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J Shin

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Apr 8, 2010, 3:48:24 PM4/8/10

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#1. How do I theoretically explain why the period is twice the
distance btwn the neighboring troughs?

I did find out the x(t) by finding particular solution and using trig
identity 2sinAsinB=cos(A-B)-cos(A+B).

but I do not know what else to do

Professor Laugesen

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Apr 9, 2010, 10:50:54 AM4/9/10

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Jay,

Correct: first you find the solution x(t) (complementary plus
particular) and then you rewrite it using a trig identity. You might
find it easier to use a "sum-to-product" trig identity:
http://www.mathwords.com/s/sum_to_product_identities.htm
e.g.
cos(x) - cos(y) = - 2 sin( (x+y)/2 ) sin( (x-y)/2 )

Then your answer will consist of a "fast" sine oscillation with a
"slowly varying" sine amplitude envelope.
The slowly varying sine gives the beating. Find the period of that
slow oscillation.