A block of mass \(M\) is attached to an ideal horizontal spring of spring constant \(k\) and rests at its equilibrium position on a frictionless horizontal surface. Two separate experiments are conducted:

In Trial 1, a lump of clay of mass \(m\) moving horizontally at speed \(v_0\) strikes and sticks to the block, causing the block-clay system to oscillate with period \(T_1\) and total mechanical energy \(E_1\).

In Trial 2, an elastic ball of mass \(m\) moving horizontally at speed \(v_0\) strikes the block, bounces elastically directly backward, and leaves the block alone to oscillate with period \(T_2\) and total mechanical energy \(E_2\).

Which of the following correctly relates \(T_1\) to \(T_2\) and compares the mechanical energy \(E_1\) to \(E_2\)?