Deriving the Correction Factor for Non-Ideal Spring Frequency Equation

[amr55533]

Homework Statement

In general, I know that you can use the equation ωn=[k/m]^0.5 to calculate the natural frequency of a hanging spring and mass system.

However, for a non-ideal spring (where the mass of the spring isn't negligible) a correction factor is added to the equation and it becomes:

ωn=[k/(m+ms/3)]^0.5

where k is the spring constant, m is the mass of the hanging mass, and ms is the mass of the spring.

How would you derive the ms/3 correction factor in this equation? I'm trying to prove that the equation is viable.

Thanks!

 

[rude man]

Try this: http://www.mathrec.org/old/2001dec/solutions.html