Simple Harmonic Motion: What is Superposition of SHM?

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SUMMARY

The discussion focuses on the concept of superposition in Simple Harmonic Motion (SHM), specifically how two SHM waves can coexist in the same system. A practical example is provided with a vibrating string, where a low-frequency sinusoidal wave is superimposed with a high-frequency wave. The linear behavior of the string ensures that the resulting motion is a combination of both waves, demonstrating the principle of superposition. This principle applies not only to mechanical waves but also to electromagnetic and sound waves.

PREREQUISITES
  • Understanding of Simple Harmonic Motion (SHM)
  • Knowledge of wave properties and behavior
  • Familiarity with linear systems in physics
  • Basic concepts of wave superposition
NEXT STEPS
  • Explore the mathematical formulation of wave superposition
  • Study the principles of linear wave theory
  • Investigate applications of superposition in electromagnetic waves
  • Learn about the effects of wave interference in sound waves
USEFUL FOR

Students of physics, educators teaching wave mechanics, and anyone interested in the principles of wave behavior and superposition in various physical systems.

Zubair Ahmad
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What does superposition of SHM means physically.. I mean how is it that two shms superpose on same system?
 
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A vibrating string, for instance: points on the string can take part in a whole spectrum of frequencies
 
Zubair Ahmad said:
What does superposition of SHM means physically.. I mean how is it that two shms superpose on same system?
Take a specific example. A string with a low frequency sinusoidal wave on it (long wavelength waves passing along it from one end to the other). Now vibrate the string with an additional low amplitude high frequency wave. Those short waves will be 'superimposed' on the larger long waves and progress along the string. If the string behaves linearly (i.e. tension at any instant is proportional to the stretch in the string) the resulting motion of any part of the string will be the result of the two waves, independently. It will consist of just two sine waves superimposed on each other. (Or for any combination of waves.)
Same for em waves, sound waves etc. etc.
 

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