Rotation and vibration of 2 particle spring system

In summary, the conversation revolves around a student struggling to solve a problem in classical mechanics without the use of Hamiltonian Mechanics. The student has attempted to use conservation of rotational momentum and energy but has ended up with a complicated equation and no progress. They have also researched online but found solutions using Hamiltonian Mechanics, which was not covered by their instructor. The student is seeking help and is asked to show their work for further assistance.
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tom131
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Homework Statement



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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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Related to Rotation and vibration of 2 particle spring system

1. What is rotation and vibration in a 2 particle spring system?

Rotation and vibration in a 2 particle spring system refer to the movement of two particles connected by a spring or multiple springs. Rotation involves the circular movement of the particles around a fixed point, while vibration involves the back-and-forth motion of the particles along the spring(s).

2. What factors affect the rotation and vibration of a 2 particle spring system?

The rotation and vibration of a 2 particle spring system are affected by the stiffness of the spring(s), the mass of the particles, and the distance between the particles. These factors determine the frequency and amplitude of the rotation and vibration.

3. How does the energy of a 2 particle spring system change during rotation and vibration?

The energy of a 2 particle spring system changes during rotation and vibration due to the conversion of potential energy (stored in the spring(s)) to kinetic energy (in the form of rotational or vibrational motion). The total energy of the system remains constant as long as there is no external force acting on it.

4. Can the rotation and vibration of a 2 particle spring system be controlled?

Yes, the rotation and vibration of a 2 particle spring system can be controlled by adjusting the stiffness of the spring(s) or changing the mass and distance between the particles. These changes can alter the frequency and amplitude of the motion, allowing for control of the system.

5. What are some real-life applications of the rotation and vibration of a 2 particle spring system?

The rotation and vibration of a 2 particle spring system have various applications in the fields of engineering, physics, and chemistry. Some examples include pendulum clocks, shock absorbers in vehicles, and molecular vibrations in chemical reactions. Understanding these motions can also lead to advancements in materials science and technology.

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