Spectroscopy hookes law, derivation?

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Discussion Overview

The discussion revolves around the equation related to Hooke's law in the context of spectroscopy, specifically questioning the presence of the variable 'c' in the equation and the use of reduced mass in calculations involving oscillators.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant expresses confusion about the equation for Hooke's law, particularly regarding the term 'c'.
  • Another participant clarifies that the equation is derived from the motion equation of a harmonic oscillator, not Hooke's law itself, and mentions that reduced mass simplifies calculations for systems with two oscillating objects.
  • A later reply identifies that 'c' is derived from the definition of wavenumber as frequency divided by 'c'.
  • Another participant points out that 'ν' is defined as frequency, not wavenumber, suggesting a potential misunderstanding in the original source.
  • One participant agrees with the correction about 'ν' but expresses skepticism about the accuracy of the original statement.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of 'ν' and its relation to wavenumber, and there is disagreement regarding the correctness of the original source's definitions.

Contextual Notes

There are unresolved questions about the definitions used in the original equation and the implications of using reduced mass in the context of oscillators.

popopopd
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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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