About the natural frequency f of the springs

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Question Lewis 2022/9/2(Fri) 1:17

Hi ive been looking at finding the natural frequency of a spring without a weight attached, i Found this Formula “For f=i/2×√(k/m) described in JIS, it is a calculation formula for calculating the natural frequency f of the spring, and m represents the mass of the spring.” Any chance you could let me know what the “i” in the equation stands for.

Id really appreciate any insight you can offer.
Thanks, Lewis

Answer Tokai Spring 2022/9/3(Sat) 11:22

Dear Lewis,

Thank you very much for your question!
Please find attached the formula (formula 15) for the natural frequency of springs from JIS. (Our apologies it is in Japanese.)
In this formula,
– If both ends are fixed or free, a=i/2,
– If one end is fixed and the other is free, a=(2i-1)/4
– i=1, 2, 3… It is a value that changes depending on the order when considering the natural frequency.

We hope it helps.

Best regards,

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