Floating test tube oscillating on water: finding the period

[Hareesh]

Problem related to Simple Harmonic Oscillations

A test tube floats, mass 20gm is set into vertical oscillations on the surface of the water. If the external diameter of the tube is 2.5cm, show that the vertical oscillations are SHO and find period of oscillations.
I found it that it attains a simple harmonic motion but I cannot make a equation for it trying for it my best.

 

[HallsofIvy]

Do you always expect to "find" answers somewhere? How about doing it yourself? If you press a float "x" cm into the water, what is the upward force on it?

What is the speed of an object falling through a V shaped tube at any point. "Conservation of Energy" should give that easily.

 

[tiny-tim]

Hi Hareesh!

I found it that it attains a simple harmonic motion …

How did you prove that without an equation?

("shm" doesn't just mean "periodic")

Hint: again, use Newton's second law F = ma to relate the forces on the test tube to its position.

What do you get?