$$m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = 0$$
$$ \newcommand\dd[2]{\mathrm{d}^{#1} #2} \newcommand\dv[3]{\frac{\mathrm{d}^{#1} #2}{\mathrm{d} #3 ^{#1}}} \newcommand\pdv[3]{\frac{\partial^{#1} #2}{\partial #3 ^{#1}}} $$
smooth = f() is continuous and f’() is continuos
$\dot{x} = f(x)$ $$f(x) = -\frac{dV}{dx}$$
$$\dv{}{V}{x} \dv{}{x}{t} = -f(x) * \dot{x} = -f(x) * f(x)$$