Spectroscopy hookes law, derivation?

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SUMMARY

The equation for Hooke's Law in the context of spectroscopy is defined as 1/(2πc) * sqrt(k/m_reduced), where 'c' represents the speed of light. The discussion clarifies that the use of reduced mass simplifies calculations for systems with two oscillating objects, making it more efficient than using a single object's oscillation around an equilibrium position. The confusion regarding the term 'c' is resolved by referencing the definition of wavenumber as v/c, where 'v' is frequency. This highlights the importance of understanding the relationship between frequency and wavenumber in harmonic oscillators.

PREREQUISITES
  • Understanding of Hooke's Law and harmonic oscillators
  • Familiarity with the concept of reduced mass in physics
  • Knowledge of wave properties, specifically frequency and wavenumber
  • Basic principles of spectroscopy
NEXT STEPS
  • Study the derivation of the harmonic oscillator equation in classical mechanics
  • Learn about the application of reduced mass in multi-body systems
  • Explore the relationship between frequency and wavenumber in wave mechanics
  • Investigate the principles of spectroscopy and its mathematical foundations
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Physics students, researchers in spectroscopy, and anyone interested in the mathematical foundations of harmonic oscillators and their applications in physical systems.

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hi, i am a lillte confused why the equation for hookes law is

1/(2pi*c)*sqrt(k/m_reduced)?

where does c come from?

http://www.massey.ac.nz/~gjrowlan/intro/lecture5.pdf

- slide 8.
Untitled-1.png


also, is there any particular reason why we use reduced mass?
 
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This is not a Hooke's law, rather a result you can get by solving the motion equation for an oscillator assuming it obeys Hooke's law (so it is a harmonic oscillator).

I don't see where the c comes from either. Using reduced mass makes calculations much easier for the system made of two oscillating objects (as compared to the system containing one object oscillating around some equilibrium position).

Moving thread to physics.
 
Borek said:
result
Ah I found it. by definition wavenumber is v/c and that gave the equation 'c'
 
They stated ν is frequency, not wavenumber.
 
Borek said:
They stated ν is frequency, not wavenumber.
yeah thanks, they did. I think they are wrong.
 

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