The spring constant of the spring shown in Diagram 1 is $k$. The block, with mass $m$, is pulled cm to the right and is then released. The block slides back and forth across the frictionless floor, in simple harmonic motion. The resulting period of oscillation for the mass-spring system is $T_1$.
An identical spring is added end to end with the first spring, as shown in Diagram 2.
Determine the period of oscillation, $T_2$, for the 2-spring system, if the block is pulled to the right and released.