A lighter than air prolate ellipsoid moves in air with constant speed (U). If this air vehicle

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A lighter than air prolate ellipsoid moves in air with constant speed \(U\). If this air vehicle oscillates simple harmonically about its center with a small amplitude \(\mathrm{A}\) in a vertical plane then find the time dependent surface downwash expression at the 

(i) shoulders,

(ii) at the front end rear ends.

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