Alex's Assignment

Alex's Fourier Project

I chose to do my LNA project on a spring mass and dampener system such as what you would find on an automobile. As shown on the picture we have a mass (M), spring (K), and dampener (D).

Equations

The first thing I need to do is write down the general equations for the Fourier Series:

$\begin{array}{rl}x(t)& =x(t+T)=a_0+\sum _{n=1}^{\mathrm{\infty }}{a}_n\cos (n{\omega }_{0}t)+b_n\sin (n{\omega }_{0}t)\\ {\omega }_0& =2\pi f_0\\ a_0& =\frac{1}{T}\underset{0}{\overset{T}{\int }}f(t)dt\\ a_n& =\frac{2}{T}\underset{0}{\overset{T}{\int }}f(t)\cos (n{\omega }_{0}t)dt\\ b_n& =\frac{2}{T}\underset{0}{\overset{T}{\int }}f(t)\sin (n{\omega }_{0}t)dt\\ \end{array}$

If odd function, $a_n=0$

If even function, $b_n=0$

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Now that we have the basic equations for a Fourier Series we can begin to calculate for the spring dampener system.