Fouriers Theorem

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Fouriers Theorem
Beats????
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Fourier Series Periodic Functions
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Why this works!

• Fouriers Hammer say you wanted to find A2
• Multiple each term by cos(2wt) and time average.

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Example
Note
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Coefficients
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Example
Time Domain
Frequency Domain
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Demos

• Mathematica
• Logger Pro

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Odd and Even Functions
Odd
Even
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Odd and Even Functions
Even
Odd
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Fourier Transforms
Spectral Density
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Dirac Delta Function
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Spectral Density of a Delta Function
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What if Spectral Density is a Delta Function
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Heavyside Step Function
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Table of Fourier Transforms (1.15.1)
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So What????
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Example 1.15.6

• A simple oscillator at rest is struck with a
  force F(t) (F) 1(t) where F 1 N. Find the
  displacement and speed of the oscillator using
  section 1.15.