An object of mass \(m\) on a horizontal frictionless surface is attached to a non-linear spring that exerts a restoring force of magnitude \(F = bx^3\) on the object, where \(b\) is a positive constant and \(x\) is the displacement from equilibrium. The object is initially released from rest at amplitude \(A_1\) and oscillates with period \(T_1\). The experiment is repeated with an initial release from rest at amplitude \(A_2 = 2A_1\), resulting in a period \(T_2\). Which of the following correctly compares \(T_2\) to \(T_1\) and provides the correct physical justification?