1. Fourier’s Theorem Beats????

2. Fourier Series – Periodic Functions

3. Why this works! Fourier’s Hammer – say you wanted to find A 2 Multiple each term by cos(2  t) and time average.

4. Example f(t) 1 -2   t 22 Note:

5. Coefficients

6. Example f(t) 1 -2   t 22 Time Domain Frequency Domain

7. Demos Mathematica Logger Pro

8. Odd and Even Functions Even Odd

9. Odd and Even Functions Even Odd

10. Fourier Transforms Spectral Density

11. Dirac Delta Function

12. Spectral Density of a Delta Function

13. What if Spectral Density is a Delta Function

14. Heavyside Step Function

15. Table of Fourier Transforms (1.15.1)

16. So What????

17. 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.