Question:
A particle of mass m moves in the xy plane with potential energy U(x,y)=−k2x2+y2. The closest point to the origin (x=0,y=0) during its motion was at a distance d, and the particle's speed at that point was v=0. Which of the following statements is true regarding the path of the particle after a long time t (t≫d/v)?
(A) The particle's trajectory will be circular.
(B) The particle's trajectory will be asymptotic to a straight line pointing away from the origin.
(C) The particle will spiral outwards away from the origin.
(D) The particle will travel on a parabolic trajectory.
(E) The particle will spiral inwards towards the origin.