Acylindrical cork (area a, length l, density pc) is floating in a liquid of density pw with only a part of its length l submerged in the liquid. if the cork is pushed down by a small distance xm and then let go, what is the frequency f of the subsequent bobbing simple harmonic motion? express your answer in terms of the quantities pc, pw, a, l, and g.

Explanation:

Given

density of cork

density of water

L=Length of cylinder

If initially x length is under water

At equilibrium

After giving push

where a  is acceleration of system

and

thus

thus

and

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement

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