What is the difference between SHM and HM ?

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Discussion Overview

The discussion explores the differences between Simple Harmonic Motion (SHM) and Harmonic Motion (HM), including definitions and characteristics of each type of motion. It addresses both theoretical and conceptual aspects of the topic.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants note that SHM is often used to refer specifically to purely sinusoidal behavior, while HM may encompass a broader range of regularly repeating behaviors that can include multiple frequencies.
  • One participant mentions that complex harmonic motion arises from the combination of multiple simple harmonic motions, using musical chords as an example.
  • Another participant defines SHM as a motion where the restoring force is proportional to the displacement, suggesting a mathematical definition involving sinusoidal functions.
  • There is a perspective that 'harmonic' is synonymous with periodic, while 'simple' indicates that the displacement is a mathematically simple function of time.

Areas of Agreement / Disagreement

Participants express differing views on the definitions and implications of SHM and HM, indicating that multiple competing interpretations exist without a clear consensus.

Contextual Notes

Some definitions and assumptions about the terms may be context-dependent, and the discussion does not resolve the nuances of how SHM and HM are applied in various scenarios.

linuxpie
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What is the difference between Simple Harmonic Motion and Harmonic Motion ?
and How do we define the motion of a system is SHM ?

Thank you !
 
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Sometimes they are used interchangably. SHM is usually taken to mean purely sinusoidal behavior. "harmonic motion" could simply mean regularly repeating behavior, but could consist of multiple frequencies (fundamental, overtones, undertones, additional fundamental excitations, etc)
 
Welcome to PF!

linuxpie said:
What is the difference between Simple Harmonic Motion and Harmonic Motion ?

Hi linuxpie ! Welcome to PF! :smile:

See http://en.wikipedia.org/wiki/Complex_harmonic_motion:
Complex harmonic motion occurs when a number of simple harmonic motions are combined.

Chords in music are an example of this phenomenon.
and How do we define the motion of a system is SHM ?

SHM is where the restoring force is proportional to the displacement (or look up wikipedia! :wink: ).
 
linuxpie said:
What is the difference between Simple Harmonic Motion and Harmonic Motion ?
and How do we define the motion of a system is SHM ?Thank you !
My understanding is that 'harmonic' is synonymous to periodic, and the 'simple' means that the displacement (from the origin) is a sinusodal function of time - i.e., a mathematically simple function. For example x(t)=Acos(wt+[tex]\phi[/tex]), where A,w and [tex]\phi[/tex] are constants. This is equivalent to the definition that tiny-tim gave above.
 
Thank you all !
 

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