# Resonant Frequencies from Fourier Analysis

1. Feb 1, 2013

### Kyxha

I did fourier analysis on a set of force data from a vibrating string. In my graph of magnitute and frequency, I'm getting major peaks at 62.1 Hz and 249.0 Hz.
There is a tiny blip in the data at 125 Hz and nothing at 186 Hz.

I have two questions. Do the peaks at 62.1 and 249 mean that those are the predominant frequencies that the string is vibrating at? And if so why wouldn't there be a more dominant peak at 125 Hz or 186 Hz, two of the other resonant modes of this string. What about a system would cause the string to skip vibrating at such frequencies?

2. Feb 1, 2013

### AlephZero

Yes, it is vibrating at those frequencies. It may be vibrating at other frequences as well - see (2) below.

The resonant modes of the string tell you the vibration modes that are possible, but:
(1) the string won't vibrate in a particular mode unless the forces acting on it make it vibrate in that mode.
(2) you may be measuring the force in the wrong place to detect vibration in some modes. That might be easier to understand if you think about measuring displacement not force. For example, if you measured the displacement of the string at its mid point, you would only "see" modes 1, 3, 5, etc, because modes 2, 4, 6 etc have a node at the mid point and there is no motion there.

You didn't give any details of the experiment, but try changing the positions along the length of the string where you apply the force to make it vibrate, and where you measure the force.

3. Feb 1, 2013

### Kyxha

The driving force is actually caused by "stick and slip" of a 0.2Kg sled on a surface. The sled is connected to a load cell with a string and the surface moves under the sled, and the cell basically measures the tension in the string. The load cell samples the tension at 800measurements/second.
I was using a plastic cord to connect the sled to the load cell and now I'm using a steel cable. Ever since the change of strings I have noticed that my data (force vs time) actually looks like a vibrating string. That's what motivated me to try and find the frequency of vibration. Even when I was using the pastic string I imagine that the data actually did represent a vibrating string, it just wasn't apparent to me. I'm not sure why switching to a steel cable made this easier to see? It's almost like the waveform in my data got stretched out so I could see the individual peaks and valleys. Do you think it could be because of the increase in linear density?
I'm also not sure if finding the frequency will tell me anything interesting or useful about properties of the surface the sled is sliding across, I think I'm mostly doing this out of curosity.

4. Feb 1, 2013

### AlephZero

When the sled slips, you will excite axial vibrations of the wire.

I would expect that in your experiment, each "slip" will excite several vibration modes which will decay quite fast. The time interval between each "slip" will depend on the speed of the moving surface. What you see in the fourier analysis will depend on whether the time between the "slips" matches a resonance of the mass on a spring, or not.

Varying the speed of the moving surface might give you some insight into what's happening. Also, you could try measuring the movement of the sled with an accelerometer and see if that matches the force in the wire. That would show if the dynamics of the wire is affecting the behaviour of the whole system.

The plastic wire was probably more flexible than the steel, so you might see the same effect with plastic at lower frequencies, if you reduce the speed of the moving surface.

5. Feb 1, 2013

### Kyxha

Ahh I can see this a lot clearer now, your posts are very insightful, thank you.
The time that it takes to complete one cycle of stick and slip will either produce constructive or destructive interference of the waves in the cord, or some combination of the two...I think.
Also I did Fourier analysis for a few different surfaces keeping all the other variables the same. I almost always get two main peaks. A medium sized one(that is always the first peak) and one double it's height that is always 4x the frequency of the medium one.

I think that is curious because if we consider the first peak to be mode 1 (which I think it is) then I would expect to measure mode 3 or 5 under the same conditions. But it seems that I am measuring mode 1 and mode 4 and the mode 4 peak is always about twice the height of mode 1. I'm not looking for an explanation for all this, just curious if you have any thoughts about it.
I looked around a bit to see if I could find anything on relative peak heights in Fourier analysis. Does a peak that is twice the height of another occur twice as often?

I like the idea of attaching an accelerometer to the sled. I might try that and then match the accelerometer data up to the force measurements and see if I can learn anything from it.

6. Feb 1, 2013

### Kyxha

I thought about it and I think I should phrase it...why are the first and fourth modes always the ones that get excited.

7. Feb 1, 2013

### AlephZero

This is just a guess - but what would the force look like if the sled is "stuck" for a time 3t, then "slips" for time t, then "sticks" again?

It might help to plot some of the data in the time domain, to see how regular or irregular to motion is.