Where does natural frequency comes from?

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SUMMARY

Natural frequency is an intrinsic property of physical bodies, determining how they vibrate and resonate, as illustrated by examples like vibrating strings and the Tacoma Bridge. These frequencies are crucial in control systems, influencing the design of controllers. The origin of natural frequencies is linked to boundary conditions and the wavelengths that fit within a given geometry. Understanding the speed of sound in materials is essential for determining these frequencies.

PREREQUISITES
  • Understanding of basic physics principles, particularly oscillations and vibrations.
  • Familiarity with control systems and their design.
  • Knowledge of boundary conditions in mechanical systems.
  • Concept of wave propagation, specifically sound waves in different materials.
NEXT STEPS
  • Study the relationship between boundary conditions and natural frequencies in mechanical systems.
  • Explore the principles of resonance and its applications in engineering.
  • Learn about the mathematical modeling of vibrations using differential equations.
  • Investigate resources on wave mechanics, focusing on sound propagation in various materials.
USEFUL FOR

Students of physics, engineers designing control systems, and anyone interested in the principles of vibrations and resonance in physical systems.

ramzerimar
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I know everything has a natural frequency that is a intrinsic property to the body in question. For example, a string vibrating has the largest amplitudes when it's vibrating near it's natural frequency, and the same thing happens with other things too (like the Tacoma Bridge).

Natural frequencies also play a important role in control systems. Systems have natural frequencies that you have to take into account when you are designing controllers for them.

While I understand reasonably well how natural frequencies "work", I can't really grasp where do they come from. I mean, is there a reason to why every body has a natural frequency? And why systems have large amplitude oscillations when in resonance?
 
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The easiest answer is that they come from the boundary conditions.

Zz.
 
It has to do with what wavelengths fit in the given geometry and give rise to resonance. Using the speed of e.g., sound, in the object, the frequency is determined.
 
Is there any book I could refeer to so as to learn more on the subject?
 

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