- #1

Alettix

- 177

- 11

T

^{2}= 1/(4π

^{2}k)*m

where T is the period, k the springconstant and m the mass of the object on the spring. This is usually acquired by setting up a force-equation for the object and solving the obtained differentialequation.

However, the mass of the spring itself isn't included in this formula. So today, I stumbled across the following formula for the period of SHM:

T

^{2}= 1/(4π

^{2}k)*(m+1/3m

_{0})

where m

_{0}is the mass of the spring.

My question is, do any of you know how this formula is derived? I understand that the "whole mass" of the spring won't affect the period of the motion, because every part of the spring doesn't have the same acceleration (not the same force equation). What I wonder about is why it's exactly 1/3.

Thank you! :)