Frequency of a wire/spring system?

[Liam B]

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

 

[DEvens]

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?

 

[Liam B]

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

And this gives the 73Hz.
My Setup:

This is the end with the spring. The other end is fixed.

 

[nasu]

And how did you measure the tension?

 

[Liam B]

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.