Can the Frequency of Oscillations Measure Fluid Density in a Loaded Test Tube?

[garytse86]

I am stuck in this question:

A loaded test tube of mass m is floating in a fluid. The test tube has a cross-sectional area A and fluid has density p.

Comment on the feasibility of using the frequency of oscillation of the tube to measure the density of the fluid.

I would say this is feasible because although there is damping due to resistance of the fluid, the frequency is the same because the motion is simple harmonic, is this correct?

Thanks.

 

[Tide]

How do you know the motion is simple harmonic? :-)

 

[garytse86]

well this is under the section oscillations and waves, so should I state the assumption is that the motion is simple harmonic?

 

[Tide]

You don't have to assume. You can show it!

Basically, two forces act on the test tube, the gravitational force which doesnt' change and the buoyant force which depends on the volume of the water displaced by the test tube. Since the test tube has a uniform cross section the volume of water displaced varies linearly with the depth of the test tube's immersion into the water. Therefore, the motion will be simple harmonic!

 

[garytse86]

oh right, thanks very much!