Fourier’s Theorem Beats????

Fourier Series – Periodic Functions

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

Example f(t) 1 -2   t 22 Note:

Coefficients

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

Demos Mathematica Logger Pro

Odd and Even Functions Even Odd

Odd and Even Functions Even Odd

Fourier Transforms Spectral Density

Dirac Delta Function

Spectral Density of a Delta Function

What if Spectral Density is a Delta Function

Heavyside Step Function

Table of Fourier Transforms (1.15.1)

So What????

Example 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.