Rotation and vibration of 2 particle spring system

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SUMMARY

The discussion centers on solving a problem involving the rotation and vibration of a two-particle spring system using only Newtonian mechanics, as per the instructor's requirements. The participant attempted to apply conservation of rotational momentum and energy but encountered a complex equation involving multiple variables and high-order derivatives. The challenge lies in avoiding Hamiltonian mechanics, which has not been covered in the course. The participant seeks assistance to progress in solving this problem.

PREREQUISITES
  • Understanding of Newtonian mechanics
  • Familiarity with conservation laws (momentum and energy)
  • Knowledge of cylindrical coordinate systems
  • Basic proficiency in solving differential equations
NEXT STEPS
  • Research techniques for solving problems in cylindrical coordinates
  • Study conservation of energy and momentum in rotational systems
  • Explore methods for simplifying complex multi-variable equations
  • Review introductory materials on Hamiltonian mechanics for context
USEFUL FOR

Students studying classical mechanics, particularly those focusing on rotational dynamics and energy conservation, as well as anyone seeking to strengthen their problem-solving skills in physics without advanced mechanics.

tom131
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Homework Statement



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Homework Equations

The Attempt at a Solution



Is it possible to solve this problem without using Hamiltonian Mechanics (just by Newtonian). My instructor expects use to solve this problem without any knowledge of any advanced classical mechanics. I tried to solve this problem using conservation of rotational momentum and conservation of energy. As the question suggests, I set my equation for kinetic energy in terms of cylindrical coordinate variables. Then I ended up with a very complicated equation with multi -variables and high order derivatives. I'm so confused .. I have been working on this one problem for like three hours, and I don't see any progress. I looked up online to see questions similar to this, but they all use Hamiltonian Mechanics, which my instructor never covered.[/B]
 
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