Help me in problem related to simple harmonic oscillations

AI Thread Summary
The discussion focuses on a problem involving a test tube floating and oscillating vertically in water, with a mass of 20 grams and an external diameter of 2.5 cm. Participants confirm that the motion is simple harmonic oscillation (SHO) but struggle to derive the equation for it. Suggestions include using Newton's second law to relate forces to the position of the test tube and considering the upward force when the tube is submerged. The importance of applying conservation of energy principles is also highlighted for understanding the motion. The conversation emphasizes the need for self-derived solutions rather than relying solely on external answers.
Hareesh
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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.
 
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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.
 
Hi Hareesh! :smile:
Hareesh said:
I found it that it attains a simple harmonic motion …

How did you prove that without an equation? :confused:

("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? :smile:
 

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