The derivation of damped frequency and natural frequency formula

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SUMMARY

The equation for damped frequency, represented as ωd=ωn√(1-ζ²), is derived from the principles of the damped harmonic oscillator. The natural frequency (ωn) and the damping ratio (ζ) are critical parameters in this derivation. The formula illustrates how damping affects the oscillation frequency of a system. For further details, refer to the comprehensive explanation available on the Wikipedia page for the damped harmonic oscillator.

PREREQUISITES
  • Understanding of harmonic oscillators
  • Familiarity with natural frequency and damping ratio concepts
  • Basic knowledge of differential equations
  • Ability to interpret mathematical formulas
NEXT STEPS
  • Study the principles of harmonic oscillators in physics
  • Learn about the derivation of the damping ratio (ζ)
  • Explore applications of damped harmonic oscillators in engineering
  • Review the mathematical techniques for solving differential equations
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Students and professionals in physics, engineering, and applied mathematics who are interested in the dynamics of oscillatory systems and their damping characteristics.

tingyuau
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Can someone derive for me the equation ωd=ωnsqrt(1-ζ2)

Thanks
 
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