# What is the difference between SHM and HM ?

• linuxpie
In summary, Simple Harmonic Motion (SHM) and Harmonic Motion are often used interchangeably, but SHM specifically refers to sinusoidal behavior while harmonic motion can involve multiple frequencies. SHM is defined as a motion where the restoring force is proportional to the displacement.

#### linuxpie

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 !

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!

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! ).

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+$$\phi$$), where A,w and $$\phi$$ are constants. This is equivalent to the definition that tiny-tim gave above.

Thank you all !