Time period of oscillation of a pole floating

[zorro]

Time period of oscillation of a pole floating...

Homework Statement

A pole is floating in a liquid with 80cm of its length immersed. It is pushed down a certain distance and released. What is its time period of vertical oscillation?

The Attempt at a Solution

I think the information given is insufficient. They should have given full length of the rod or area of its cross section.

When displaced by a small distance x, restoring force, ma=Vρg=Axρg
w²=Aρg/m=Aρg/ALσ, where L is the full length of the rod and σ is its density. I can't proceed any further without knowing the values.

The answer given is 4π/7 s.

 

[zorro]

Anyone?

 

[ashishsinghal]

When displaced by a small distance x, restoring force, ma=Vρg=Axρg

The restoring force will not be equal in both the directions. Once excess buoyant force and once excess weight would act.

 

[ashishsinghal]

yeah, atleast full length must be given. Other 80cm has no meaning

 

[zorro]

The restoring force will not be equal in both the directions. Once excess buoyant force and once excess weight would act.

There is a net restoring force only in the upward direction.

 

[ashishsinghal]

During the oscillation when the float will be above its equilibrium position, then?
It would be nice if you post a diagram.

 

[ehild]

When displaced by a small distance x, restoring force, ma=Vρg=Axρg
w²=Aρg/m=Aρg/ALσ, where L is the full length of the rod and σ is its density. I can't proceed any further without knowing the values.

Use the condition that 0.8 m is immersed in equilibrium.

ehild

 

[zorro]

During the oscillation when the float will be above its equilibrium position, then?

I understand what you mean now. When the pole is pushed downward, there is a net restoring force acting in the upward direction and that is sufficient to write the equation for S.H.M. When it is above the equilibrium position, there is a different restoring force but its magnitude is same as the previous one.

Use the condition that 0.8 m is immersed in equilibrium.
ehild

where?

 

[ehild]

You get information about the length and density of the rod from the equilibrium condition.

ehild

 

[zorro]

I got it. Thanks!