# A U—tube of constant cross-sectional area A consists of a horizontal section connected at either end to two vertical sections. Suppose that the tube is ﬁlled with an incompressible liquid of mass density p.

A U—tube of constant cross-sectional area A consists of a horizontal section connected at

either end to two vertical sections. Suppose that the tube is ﬁlled with an incompressible

liquid of mass density p. Let the total length of the liquid column be I. (Where I exceeds the

length of the horizontal section.) Suppose that the surface of the liquid in one of the vertical

sections is initially displaced (vertically) a small distance h from its equilibrium position.

Show that the surface displacement subsequently executes simple harmonic motion at the

angular frequency w = «(2 g/l, Where g is the acceleration due to gravity.

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