An ideal spring, with a relaxed length of $50 cm$, hangs from the ceilling. A uniform solid block of mass $m$ is suspended, as shown in Diagram 1. The block is at rest, and the distance from the ceiling to the top of the block is $54 cm$.
Spontaneously, $1/3$ of the block breaks away and falls straight down, causing the system to begin to oscillate with simple harmonic motion, as shown in Diagram 2.
Determine the period of oscillation $T$.