A particle of mass m = 1 moves along the x-axis under a force whose potential is:
V(x) = (1 - x^2)*e^(-(x^2)/4)
Sketch the function V against x, find equilibrium positions and stability. Determine the periods of small oscillations about the stable equilibrium point(s). If the particle is started at x = sqrt(5) with speed U, determine the ranges of U for which the particle (i) oscillates, (ii) escapes to
+infinity and (iii) escapes to −infinity.