A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column-I (a and U0 are constants). Match the potential energies in column-I to the corresponding statement(s) in column-II.
`{:((A),U_1(x)= (U_0)/(2)[1-(x/a)^(2)]^(2),(P),"the force acting on the particle is zero at x = a."),((B),U_2(x)= (U_0)/(2)(x/a)^(2),(Q),"the force acting on the particle is zero at x = 0."),((C),U_2(x)= (U_0)/(2)(x/a)^(2)exp[-(x/a)],(R),"the force acting on the particle is zero at x = 0."),((D),U_4(x)= (U_0)/(2)[x/a - 1/3 (x/a)^3],(S),"The particle experiences an attractive force towards x = 0 in the region | x | < a"),(,,(T),"The particle with total energy" (U_0)/4 " can oscillate about the point"x = -a.):}`