A block of mass \(m\) is attached to an ideal horizontal spring with spring constant \(k\) on a frictionless surface and oscillates in simple harmonic motion with amplitude \(A\), period \(T_0\), and maximum acceleration \(a_{\text{max}, 0}\). The system is modified by replacing the block with one of mass \(2m\) and the spring with one of spring constant \(4k\), while maintaining the same oscillation amplitude \(A\). Which of the following correctly relates the new period of oscillation \(T\) and new maximum acceleration \(a_{\text{max}}\) to their initial values?