Sloshing in a Rectangular Container: Finding Time Period

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Homework Help Overview

The discussion revolves around a physics problem involving the sloshing of water in a rectangular container. The original poster seeks to determine the time period of the sloshing mode after the container is slightly disturbed, while assuming the water surface remains practically flat during the motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply an energy equation involving rotational and gravitational potential energy but expresses confusion about its applicability. Some participants question the relevance of certain terms in the equation, particularly regarding the center of mass and its movement. Others encourage the poster to clarify their understanding of the water's behavior during sloshing.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the original poster's approach. There is no clear consensus yet, as participants are still seeking clarification and further insights into the problem.

Contextual Notes

There appears to be some misunderstanding regarding the physical setup and the dynamics of the water's motion, which may affect the formulation of the energy equation. The original poster acknowledges potential confusion about the question itself.

crotical
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Homework Statement


A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode. take width to be

The Attempt at a Solution



I tried to put up the equation of energy , and differentiating it .

θ be the angle made by surface and the slant made by surface after slosh ,
1/2 Iω2 + mgh = U

but this doesn't lead me anywhere, can some one please tell what should i add in the energy equation .
 
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welcome to pf!

hi crotical! welcome to pf! :wink:

what does mgh have to do with it?

surely the centre of mass isn't moving?​
 
Then what should i add to the Energy equation
 
love o:)
 
So that means , no help ?
 
crotical said:
A rectangular container partly filled with water up to height , after being slightly disturbed , the urface of water begins to slosh . Assume that the water surface remains practically flast during sloshing , find the time period of the sloshing mode.

θ be the angle made by surface and the slant made by surface after slosh ,
1/2 Iω2 + mgh = U

but this doesn't lead me anywhere, can some one please tell what should i add in the energy equation .

i think I've misunderstood the question :redface:

what exactly is the water doing?​

show us your full equation anyway :smile:
 
Water is in a cup , find SHM of the surface , if slightly displaced
 
Tiny ?
 
crotical?

your equation?
 

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