What is Resonance? (Part 2)

This article is a follow on from What Is Resonance? (Part 1) and answers some of the issues not covered in that post.

How do you find the resonant frequency in the real world? What do you do when there is a situation with multiple peaks in the frequency domain data? How do you know the frequency you have found is a resonant frequency?

To answer any and all of the above questions can often be very simple, but sometimes, not so. Often there is a single clear peak in the frequency domain data that is easy to pick out, but sometimes there are many peaks. How do you find what you’re looking for in this case?

First, we have to explain what we are studying. In this article we will look at frequency response functions and how they are used to find a resonant or resonant frequencies.

For example, if we have a frequency response function from a hammer impact test, how do we find the resonance?

If we look at the magnitude or modulus part of the frequency response function in a raw format we’ll see something like that shown in Figure 1.

Modulus part of transfer function
Figure 1: Modulus part of frequency response function

There is only one peak in this case, but how do we know for sure this is the resonance?

From the signal shown in Figure 1 we cannot say. We can make a best guess based on our understanding of the structure or part under test, but that is all.

So what do we need to make a judgement? The answer is phase.

With both the modulus and the phase it is possible to make a decision upon which frequency is the resonant frequency.

If we look closely at the modulus and phase signals shown in Figure 2, we can see the frequency peak, but we can also see a peak in the corresponding phase.

Modulus & phase part of the transfer function
Figure 2: Modulus & phase part of the frequency response function

In Figure 3 we have zoomed in on the x scale to see the data more clearly. It is now possible to pick out the peak at 1758Hz. We have highlighted it using the DATS cursor marker function.

Modulus & phase of transfer function (x scale zoomed)
Figure 3: Modulus & phase of frequency response function (x scale zoomed)

Pay careful attention to the plots of the peak and it is clear to see that the peak at 1758Hz does have a corresponding phase switch of 180 degrees. This is a classic sign of a resonance, a large peak associated with a flipping in phase.

Generally, an engineer will not see data this clear or obvious, but this article is intended to show the concept of how you would find a resonance in a simple system.

Modulus & phase of transfer function (modulus shown on log scale)
Figure 4: Modulus & phase of frequency response function (modulus shown on log scale)

Further plots of this form would classically be shown on a logarithmic scale (or log scale for short). Figure 4 shows the same data on a log scale. Here both the resonance and the anti resonance are shown. The anti resonance was not visible at all on the linear scale, but shows itself and its phase inversion clearly in the log scale at 1689Hz. If not for viewing the data in the logarithmic form, this additional information would have been missed by visual inspection.

Further Reading & Viewing

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James Wren

Former Sales & Marketing Manager at Prosig
James Wren was Sales & Marketing Manager for Prosig Ltd until 2019. James graduated from Portsmouth University in 2001, with a Masters degree in Electronic Engineering. He is a Chartered Engineer and a registered Eur Ing. He has been involved with motorsport from a very early age with a special interest in data acquisition. James is a founder member of the Dalmeny Racing team.
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Tylor Liu
8 years ago


Please tell me the reason it have to be 180 deg change when resonance?

what if the amplitude peak is not with the phase change, what is the peak normal means in physical phenomenon?

3 years ago
Reply to  James Wren

If the natural frequency is at 90 degree phase shift why figure 3 indicates 180 degree phase shift at resonance.

If the structure is critically damped with no peak observed, can we read frequency with 90 degree phase shift to predict the resonance frequency of the un-damped structure?

Farid Arvani
Farid Arvani
8 years ago

What is the physical interpretation of anti-resonance?

Ryan Agustino
8 years ago

how is resonance applicable to sirens?

8 years ago

How does a phase shift of 90 degrees at the resonant frequency creat such a high response? What is the physical meaning of this? Cheers

Hao Lam
7 years ago

Hello James,

I found these articles are very useful for non-experienced vibration engineers.
May I use your articles to trained our new engineers at my company.

Hao Lam

7 years ago
Reply to  Hao Lam

Hello Hao Lam

James is away from the office for a few days so I will reply for him.

We are pleased that you like the articles. You are welcome to use them for training purposes. We only ask that you state that they came from Prosig. And maybe encourage your engineers to read the blog themselves 🙂


Samruddhi Katkar
Samruddhi Katkar
4 years ago

When we are using an accelerometer and Impact hammer , FFT of Accelerometer signal(response to impact of hammer) represents Natural frequency? If yes then why to use FRF?

3 years ago
Reply to  James Wren

But in cases where we just need to find natural frequency of the object.we hit the structure with hammer and FFT of the response( accelerometer) clearly shows the amplitude is decreasing as the time passes but particular frequency does not even change slightly and from that,the one who is performing the test gets the clear picture of what natural frequency is for that object.

But in case of FRF, I would like to know what is the physical significance of the peaks in the magnitude-Frequency graph and what is the significance of the phase shift. Means how we can prove that the peaks we see in the magnitude frequency graph having corresponding phase shift of 180 degree, are natural frequencies?
In FFT, it is so clear that anyone can understand, if we are hitting the object, we can actually see decreasing amplitude but frequencies doesnt change.

3 years ago

Hi James and Chris,

Would like to know how to calculate modal mass and stiffness at a particular peak?

3 years ago

Hi James and Chris

We work on Car NVH problems using CAE. We have couple of questions.
Whenever we have issue with amplitude, more than reference or target, we check the behaviour of the structure at that frequency and in case of acoustic we see panels contributing to this particular high amplitude.
Based on high sensitive parts, when we work on design changes to improve, sometimes we don’t get any improvements even after many iterations. Sometimes we are clueless how to proceed?
Usually what would be the problems for high amplitudes? And how to root cause these and countermeasure? Please respond in vehicle point of view.
Also what approaches we need to follow to reduce amplitudes and what approach we need to follow shift frequency? In a nut shell we know applying (natural frequency as function of K and M) but to which parts we need to apply how that will effect in global values, sometimes we are not sure.
Most of the times, we are not allowed to use damping materials, and we have to work on structure, either add reinforcement, beads, modify Youngs modulus and/or change thickness. (Thickness increase in rare cases)

Would love your thoughts, please comment.x