A block of mass \(M\) is attached to an ideal horizontal spring with spring constant \(k\). The system oscillates on a frictionless surface with amplitude \(A\) and period \(T_1\). A second system consists of a block of mass \(4M\) attached to an identical spring, oscillating with amplitude \(2A\) and period \(T_2\). What is the value of the ratio \(\dfrac{T_2}{T_1}\)?