Suppose a particle of mass m is moving in one direction, horizontally, with its position given by (t). Suppose at time t = 0, the ball is at position x (0) = 0. Suppose the particle is subject to a potential given by V(x) = - ;a". The graph of this potential function is shown in the figure below, and it looks like an infinite hill (it continues on outside of the figure). When a = 0, the particle is at the very top of this potential hill. If it moves away from * = 0, it will experience a drop in the potential. (a) Newton's equation for the particle in this potential (c.f. Problem 5) is m d+2 dx This is a homogeneous 2nd order equation with constant coefficients. Using what you learned in Math 307 to find the general solution x (t) to this 2nd order equation. Then differentiate r to find p(t) = m d (b) Write Newton's equation, ma" = Ex, as a system of ist order equations in c and p, After that, write this system in the form of