Curves & Motion · Superchallenge problem

A particle in space obeys $\mathbf r''(t) = -4\,\mathbf r(t)$, with $\mathbf r(0) = (1, 0, 0)$ and $\mathbf r'(0) = \left(0,\ 2,\ 2\sqrt3\right)$. Find the maximum curvature of its path.