A particle of mass \(m\) is constrained to move along the \(x\)-axis under the influence of a conservative potential energy function given by \(U(x) = c|x|\), where \(c\) is a positive constant. The particle is released from rest at position \(x = x_0\) (where \(x_0 > 0\)) and undergoes periodic oscillations between \(x = -x_0\) and \(x = x_0\). Which of the following integral expressions correctly represents the period \(T\) of the particle's oscillation?