Cubic lattice, masses and springs, fire little mass at it.

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SUMMARY

The discussion centers on the dynamics of a cubic lattice composed of N^3 masses, M, connected by springs with constant k. When a mass, m, is fired at the lattice with velocity v, the inquiry is whether this can result in pure translational motion of the lattice with minimal vibrational energy. The analogy drawn to the Mössbauer effect highlights the desire to achieve gamma emission without generating crystal phonons. The conclusion indicates that a gentle push on the lattice results in minimal vibrations, while a forceful shove leads to both translational and vibrational energy increases.

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  • Understanding of classical mechanics principles, particularly momentum and energy transfer.
  • Familiarity with spring-mass systems and Hooke's Law.
  • Knowledge of lattice dynamics and phonon theory.
  • Basic concepts of the Mössbauer effect and its implications in solid-state physics.
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  • Explore the mathematical modeling of spring-mass systems under different force applications.
  • Investigate the relationship between translational and vibrational energy in lattice systems.
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  • Learn about phonon dispersion relations and their significance in solid-state physics.
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Physicists, mechanical engineers, and students studying solid-state physics or classical mechanics, particularly those interested in lattice dynamics and energy transfer mechanisms.

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Suppose I have a cubic lattice of N^3 masses, M, each connected to six nearest neighbors with springs of constant k free to move but at rest. Now fire a single mass, m, with velocity v at surface of the lattice such that no rotation can be imparted to the cubic lattice. Let the fired mass bounce off a single lattice mass so that both masses move in the opposite direction.

Can we fire a mass at a lattice at rest and only produce translation of lattice with no or little vibration of the lattice?

I wanted to understand if there was a classical system similar to the crystal in the Mössbauer effect where we can have gamma emission with no crystal phonons produced.

Thanks for any help!
 
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I think what I'm asking can be simplified with the following classical setup. Let there be a one dimensional lattice of N masses M, connected by springs with the whole system constrained to move on a line. Suppose we give the first mass of this system a slow gentle shove. I think the math would show that the lattice would move as a whole with very little vibrational energy being produced. But now suppose we give the first mass of the lattice a hard fast shove then it seems the math would also show that now the lattice would gain both translational and vibrational energy?
 

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