A particle of mass m kg is attached to one end A of a model spring OA of natural length L0 = 1 m and stiffness K N/m. The spring is hung vertically with the end O fixed and end A attach to the particle, which moves in a vertical line. The particle's mass, stiffness and natural length of the spring are related to the expression KL0=2mg, where g is the magnitude of the acceleration due to gravity.

It is observed that when the particle is at its highest point during the motion, its distance below O is A1/2 L0. Using the law of conservation of mechanical energy, find the distance, in m, of the particle below O when it is at its lowest point during the motion. Please show working and give your answer to 3 decimal places.