Help me in problem related to simple harmonic oscillations

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SUMMARY

The discussion focuses on a problem involving simple harmonic oscillations (SHO) of a test tube floating on water, with a mass of 20 grams and an external diameter of 2.5 cm. Participants confirm that the vertical oscillations of the test tube are indeed simple harmonic motion and suggest using Newton's second law (F = ma) to derive the equations governing the motion. The conversation emphasizes the importance of understanding the forces acting on the test tube to establish the relationship between displacement and oscillation period.

PREREQUISITES
  • Understanding of simple harmonic motion (SHO)
  • Familiarity with Newton's second law (F = ma)
  • Basic principles of fluid mechanics
  • Knowledge of oscillation period calculations
NEXT STEPS
  • Study the derivation of the period of oscillation for simple harmonic motion
  • Explore the application of Newton's second law in fluid dynamics
  • Investigate the effects of buoyancy on oscillating objects
  • Learn about energy conservation principles in oscillatory systems
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Students and educators in physics, particularly those focusing on mechanics and oscillatory motion, as well as anyone interested in the practical applications of simple harmonic oscillations in fluid systems.

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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