We can introduce two variables, $x_1 = x$ and $x_2 = \dot{x}$. Then, we can rewrite the equation as:
$$m\ddot{x} + b\dot{x} + kx = 0$$
Now, we can write the first-order equations:
$$\dot{x_1} = x_2$$
$$\dot{x_2} = -\frac{b}{m}x_2 - \frac{k}{m}x_1$$
Now, we
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