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{\bf Question}

Find the damping parameter and the natural frequency of the system
governed by the equation: $$\frac{d^2x}{dt^2} + 2 \frac{dx}{dt} +
4x = 0$$

\vspace{.25in} {\bf Answer}

$$\frac{d^2x}{dt^2} + 2 \frac{dx}{dt} + 4x = 0$$

Auxiliary equation:

General form is $m^2  2G \omega m + \omega^2 = 0$

In this case it is $m^2 + 2m + 4 = 0$

Comparing the two equations gives $\omega = 2$ so $2G \omega = 2
\Rightarrow 4G = 2 \rightarrow G = \frac{1}{2}$


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