When a particle of mass m moves on the x-axis in a potential of the form `V(x) =kx^(2)` it performs simple harmonic motion. The correspondubing time period is proprtional to `sqrtm/h`, as can be seen easily using dimensional analusis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of `x=0` in a way different from `kx^(2)` and its total energy is such that the particle does not escape toin finity. Consider a particle of mass m moving on the x-axis. Its potential energy is `V(x)=ax^(4)(agt0)` for |x| neat the origin and becomes a constant equal to `V_(0)` for |x|impliesX_(0)` (see figure). . The acceleration of this partile for `|x|gtX_(0)` is (a) proprtional to `V_(0)` (b) proportional to.A. (a) proprtional to `V_(0)`B. (b) proportional to `V_(0)/(mX_(0))C. (c ) proportional to `sqrtV_(0)/(mX_(0)`D. (d) zero`.