Simple Harmonic Motion Question

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SUMMARY

The discussion centers on the concept of simple harmonic motion (SHM) and the use of the symbol omega squared (ω²) to represent the ratio of spring constant (k) to mass (m). Participants clarify that while omega is typically associated with angular speed, its designation in this context is a mathematical convenience that simplifies the solution process. The choice of ω² is justified post-solution, as it aligns with the physical interpretation of angular speed in SHM.

PREREQUISITES
  • Understanding of simple harmonic motion principles
  • Familiarity with the concepts of spring constant (k) and mass (m)
  • Basic knowledge of angular speed and its relation to oscillatory motion
  • Mathematical skills for manipulating equations and substitutions
NEXT STEPS
  • Study the derivation of the equations of motion for simple harmonic oscillators
  • Explore the relationship between angular frequency and physical parameters in SHM
  • Investigate the implications of different values of k and m on the motion of oscillators
  • Learn about the energy transformations in simple harmonic motion systems
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the mathematical foundations of oscillatory systems will benefit from this discussion.

ThatDude
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Homework Statement



I have a question about simple harmonic motion:
upload_2015-1-27_18-15-31.png


Where it says " if we denote the ratio k/m with the symbol omega squared ... ": I know it says that they chose omega squared to make the solution simpler, but I mean, to me it doesn't really make sense. Omega is associated with angular speed, so how can they just make a relation between angular speed, k and m, as they did above, without justifying it?
 
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ThatDude said:
Omega is associated with angular speed
At the point where the substitution is made, no assumption is made about what omega will represent in the real world. When the solution is obtained, it becomes clear that it corresponds to angular speed. Of course, the choice of omega as the symbol, and ##\omega^2## as the specific substitution, is because the author knows that's how it will turn out.
 

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