6. (15 points) Consider the spring-mass system $my'' + 2y' + ky = 0$.
(a) On the $(m, k)$-plane, sketch the region corresponding to over-damping and under-damping respectively.
(b) If we randomly choose $(m, k)$ from the region $0 < m < 2$ and $0 < k < 1$, what is the probability that the system is under-damped?