Frequency of a wire/spring system?

AI Thread Summary
The discussion centers on the frequency of a wire under tension from a spring, where the calculated first mode is 73.6 Hz, but a vibration test shows 110 Hz. The discrepancy raises questions about potential errors in the calculation, particularly regarding the assumption of fixed ends versus the actual setup with one end attached to a spring. The user confirms the calculation is correct for fixed ends but acknowledges the setup may not reflect that condition, leading to a significant frequency difference. The tension was measured by hanging a 2 lb weight, which compressed the spring and defined the wire's length. The conversation highlights the importance of accurately modeling boundary conditions in frequency calculations.
Liam B
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Hi, I have a wire that is fixed on one end and is under 2 lbs (approx) of tension on the other end due to a spring. Using a fixed/fixed closed form solution I found the first mode to be 73.6 Hz. In a vibration test, we found the first mode to be 110 Hz. Does this seem reasonable and where do you think my error is coming from? The wire is made of 7x7 braided stainless steel and is .018 inches diameter.

Liam
 
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Welcome to the forum.

Maybe I could help you more effectively if you showed your work. But I do note that the ratio of the two is suspiciously close to the square root of 2. Did you drop a factor of root 2?
 
Thank you, I'm happy to be here.

No, that is a good question though. The 73 Hz. is correct and I have checked it with several different sources. It assumes however that both ends are fixed and in reality one end of the wire is attached to a spring. I just didn't think that I would get 1.5x error.

My original equation was

CodeCogsEqn.gif


And this gives the 73Hz.
My Setup:
IMG_20150612_130508.jpg


This is the end with the spring. The other end is fixed.
 
Last edited:
And how did you measure the tension?
 
nasu said:
And how did you measure the tension?
I found weight that measured 2 lbs, hung it off the end of the wire which compressed the spring on the other end, and then crimped and cut the wire at that length.
 

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