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# Simple Harmonic Motion of a Floating Object

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An object with height h, mass M, and a uniform cross-sectional area A floats upright in a liquid with density p.

a). Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium.

b). Calculate the vertical distance from the surface of the liquid to the bottom of the floating object at equilibrium.

c) Your result in part B shows that if the force is suddenly removed, the object will oscillate up and down in SHM. Calculate the period of this motion in terms of the density rho of the liquid, the mass M, and cross-sectional area A of the object. Neglect the damping due to fluid friction.

Express your answer in terms of the given quantities.

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#### Solution Preview

** Please see the attached file for the complete solution response **

a) Let the depth of the bottom of the cylindrical object from the surface of the liquid be d. The object is subjected to two forces : i) Weight Mg downwards, ii) Upward thrust of the liquid equal to the weight of the liquid displaced.

The object displaces liquid equal in volume to the volume of the immersed portion of the object.

Volume of the immersed portion of the cylindrical object = Volume of the liquid displaced = area of cross section x depth of the immersed portion = Ad ...

#### Solution Summary

This solution provides a detailed step by step solution to the given physics problem.

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