Sloshing in a Rectangular Container: Finding Time Period

[crotical]

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 .

 

[tiny-tim]

welcome to pf!

hi crotical! welcome to pf!

what does mgh have to do with it?

surely the centre of mass isn't moving?​

 

[crotical]

Then what should i add to the Energy equation

 

[tiny-tim]

love

 

[crotical]

So that means , no help ?

 

[tiny-tim]

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 …

what exactly is the water doing?​

show us your full equation anyway

 

[crotical]

Water is in a cup , find SHM of the surface , if slightly displaced

 

[crotical]

Tiny ?

 

[tiny-tim]

crotical?

your equation?​