Clarifying Young's Modulus and Stiffness Equations for Cantilever Oscillation

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SUMMARY

The discussion centers on the clarification of Young's Modulus (E) and stiffness (k) in the context of calculating the time period (T) of a cantilever's oscillation. Young's Modulus is defined as a material property that quantifies its stiffness, while stiffness (k) is a structural property that reflects the resistance to deflection. The confusion arises from the interchangeable use of these terms in equations related to cantilever oscillation. Understanding the distinction between these parameters is crucial for accurate calculations in mechanical engineering applications.

PREREQUISITES
  • Understanding of mechanical properties, specifically Young's Modulus and stiffness.
  • Familiarity with oscillation equations and their applications in cantilever structures.
  • Basic knowledge of differential equations as they relate to oscillatory motion.
  • Experience with material science concepts related to elasticity and deflection.
NEXT STEPS
  • Study the derivation of the time period formula for cantilever oscillation.
  • Learn about the relationship between Young's Modulus and stiffness in various materials.
  • Explore the impact of geometric factors on the stiffness of cantilever beams.
  • Investigate advanced topics in oscillation theory, such as damping effects in cantilever systems.
USEFUL FOR

Mechanical engineers, materials scientists, and students studying structural dynamics will benefit from this discussion, particularly those focusing on cantilever beam analysis and oscillation behavior.

zeldaspurpose
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Just want clarification on two equations.

So basically, I want to calculate the time period T of the complete oscillation of a cantilever. I use this equation.
hgNhdyiGUWA0f0WGolN4oq1Bx-NZ1iowri5CpO8veyOtjCeHwE5adN_Yd_f4nRQuMtwgetzwGduNQIVJDG8JPhi9RU_xNd3j.png

Is E equal to young's modulus or is it equal to stiffness? If it is equal to stiffness, can I use this equation to calculate the stiffness?
k =
upload_2017-6-6_17-47-32.png


Thank you in advance. :)
 
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What is your definition of the parameter that you call "stiffness?"
 
In my case, I think it is the resistance of deflection. However, when I search online that is also the definition for Young Modulus. Yet there's these two different equations which is confusing.
 

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