The Taylor series expansion of a function $f(x)$ around a point $x_0$ is given by:
$$f(x) = f(x_0) + \frac{df}{dx}(x_0)(x-x_0) + \frac{1}{2!}\frac{d^2f}{dx^2}(x_0)(x-x_0)^2 + \ldots$$ mecanica clasica taylor pdf high quality
In classical mechanics, this expansion is often used to describe the potential energy of a system near a stable equilibrium point. By expanding the potential energy function $U(x)$ around the equilibrium point $x_0$, one can write: The Taylor series expansion of a function $f(x)$
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where $k$ is the spring constant or the curvature of the potential energy function at the equilibrium point.
$$U(x) = U(x_0) + \frac{1}{2}k(x-x_0)^2 + \ldots$$