A block of mass \(m\) is attached to an ideal horizontal spring of force constant \(k\) and executes simple harmonic motion with amplitude \(A\) on a frictionless horizontal surface. At a particular position during the oscillation, the kinetic energy of the block is equal to three times its elastic potential energy. What is the ratio of the magnitude of the block's displacement from equilibrium to the amplitude, \(\dfrac{|x|}{A}\)?