In: Physics
A particle of mass m is constrained to lie along a frictionless, horizontal plane subject to a force given by F (x) = −kx + kx^3/A^2 where k and A are positive constants. The particle is projected from x = 0 to the right with initial kinetic energy T0. Find the turning points of the motion and the condition the total energy of the particle must satisfy if its motion is to exhibit turning points.
The main concept about the problem is at turning point the radial component of the velocity is zero.