An ideal spring hangs from a ceiling, attached to a block of mass, $m$, as shown in Diagram 1. The system is moving up and down, in simple harmonic motion with a period of $T_1$.
A second, identical spring is attached to the block and ceiling, as shown in Diagram 2. The block is then pulled down slightly, and released to cause the system to oscillate up and down.
Determine the new period of oscillation, $T_2$.