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# Simple Harmonic Motion: Vertical Mass Spring System Period

APPHMC-AIYIR8

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 $T$.

A

$T=0.052 s$

B

$T=0.33s$

C

$T=1.7s$

D

This problem can not be solved without knowing the original mass of the block.

E

This problem can not be solved without knowing the amount of stretch in the spring in Diagram 2.