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robmass
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Hiya can anyone show how to derive the euqation of damped frequency for a spring
ωd = ωnsqrt(1-ζ2)
ωd = ωnsqrt(1-ζ2)
How Do You Derive the Equation for Damped Frequency in a Spring System?
- Thread starter robmass
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- Damped Derivation Frequency
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SUMMARY
The discussion focuses on deriving the equation for damped frequency in a spring system, specifically the formula ωd = ωn√(1-ζ²). Participants emphasize that the process involves writing the differential equation for simple harmonic motion with damping and solving it directly, without the need for complex techniques. The key takeaway is the straightforward approach to understanding damped frequency through basic differential equations.
PREREQUISITES- Understanding of differential equations
- Knowledge of simple harmonic motion
- Familiarity with damping ratios (ζ)
- Basic physics concepts related to spring systems
- Study the derivation of the differential equation for simple harmonic motion
- Explore the concept of damping ratios and their effects on oscillations
- Learn about the applications of damped frequency in engineering systems
- Investigate numerical methods for solving differential equations in mechanical systems
Students of physics, mechanical engineers, and anyone interested in the dynamics of oscillatory systems will benefit from this discussion.
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