How Does a Liquid Oscillate in a U-Shaped Tube?

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A liquid in a U-shaped tube oscillates harmonically when displaced from equilibrium, with the difference in height between the two sides being 2x. The motion can be described by the equation a = -ω²x, indicating a restoring force proportional to the displacement. To derive the period of oscillation, one must consider the pressure difference and the effective force acting on the liquid. The discussion emphasizes the need for a systematic approach to solving the problem, including showing steps and demonstrating understanding. Ultimately, the oscillation behavior can be analyzed using fundamental principles of fluid dynamics and harmonic motion.
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Homework Statement


A liquid is placed in a U-Shaped tube. Initially both are at the same level. Total length of liquid is L. But later one side is displaced from equilibrium by X.(Difference of both sides is 2x now). Show that the water will oscillate harmonically in the form of a=-w squared x. Hence derive an expression for period of oscillation in terms of L.



Homework Equations


Pressure= hpg
F=ma


The Attempt at a Solution


Not really sure about this question...
 
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You should show at least some steps..or at least tell us any idea you might have about how to approach the problem, so we know you have spent some time on it. :)
 

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