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Classical Mechanics

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Moderate

Archmedes Principle: The Ocillating Buoy

CLMECH-YEKJA4

When a long cylindrical buoy is pushed gently down a small distance into the water it will, upon release, begin to oscillate up and down.

Ignoring friction of any kind, is this motion simple harmonic motion?

If yes, what is the period in terms of the mass, $m$, and dimensions of the buoy, $A$ and $h$ (the area and vertical height) and the density of water $\rho$?

Created for Albert.io. Copyright 2016. All rights reserved.

A

No, not simple harmonic motion.

B

Yes ,$T=2\,\pi\,\sqrt{\frac{\rho\cdot A\cdot g}{m}}$

C

Yes, $T=2\,\pi\,\sqrt{\frac{m}{\rho\cdot A\cdot g}}$

D

Yes, $T=\sqrt{\frac{m}{\rho\cdot A\cdot g}}$