(adsbygoogle = window.adsbygoogle || []).push({}); simple harmonic motion and specific gravity. PLEASE HELP!!

The problem I need help with is this: In his lecture, Dr. Dyson argued that one could determine the specific gravity of a wine in the absence of a hydrometer. To demonstrate this he constructed a 100g weighted cylinder of Length (L) and cross-sectional area (A) that floated vertically. When the cylinder was placed in a glass of wine a length (L') was submerged at its equilibrium postion. He lifted the cylinder from its equilibrium position by an amount y, released it and timed its cycles. a) show that the cylinder executes simple harmonic motion when it is released. That is show the restoring force is proportional to the cylinder's displacement from its equilibrium position.

I was able to complete the following:

FB=p(V1 + V2)g

(p=density not pressure)

V2=Ay

(y=displacement)

FB=pV1g + pAyg.

I know i have to some how prove that the Force is proportional to displacement, but I'm stuck at exactly how to prove that.

This problem actually has more parts, but I can't go onto the next parts until I prove this.

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# Simple harmonic motion and specific gravity. PLEASE HELP

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