A particle of mass \(m\) is constrained to move along the \(x\)-axis in a region where its potential energy is given by \(U(x) = \alpha x^4\), where \(\alpha\) is a positive constant. The particle is released from rest at \(x = A\) and oscillates periodically about the equilibrium point \(x = 0\). If the oscillation amplitude \(A\) is increased, which of the following statements correctly describes the effect on the period of oscillation and provides the correct physical justification?