WHY do things have a natural frequency?

So, I get that when an object oscillates due to a driving frequency equal to its natural frequency, it will resonate, but I was wondering why exactly do objects have this natural frequency? Is it a mathematical consequence of some sort?

I know also that a few factors affect it such as length, stiffness etc. but how exactly do they affect it? It just seems a little nonsensical that we can't mathematically determine it as opposed to just experimentally determining it (as far as I know, anyway).

I asked a Professor at my Manchester uni interview day, but he was like a systems Biologist and couldn't really answer me

So, I get that when an object oscillates due to a driving frequency equal to its natural frequency, it will resonate, but I was wondering why exactly do objects have this natural frequency? Is it a mathematical consequence of some sort?

I know also that a few factors affect it such as length, stiffness etc. but how exactly do they affect it? It just seems a little nonsensical that we can't mathematically determine it as opposed to just experimentally determining it (as far as I know, anyway).

I asked a Professor at my Manchester uni interview day, but he was like a systems Biologist and couldn't really answer me

(...) why exactly do objects have this natural frequency? (...)

It is modelled mathematically using simple harmonic motion.

An objects natural frequency of oscillation depends on its mass/inertia, its size and the elastic forces within it.
The simplest case is a mass on a spring. This can be modelled easily to give its natural frequency of vibration, f, as

$f = \frac{1}{2 \pi}\sqrt{\frac{k}{m}}$

m is the mass and k the stiffness of the spring.
Any physics book will have a proof of this.

A pendulum also has a natural frequency which depends on its length.

Look up simple harmonic motion. It's fundamental in physics.

I dont know either, so just another speculation:
If you imagine a ball on the end of a string, if you knock it, it will oscillate. If you were to knock it again in the middle of its oscillation, it would just oscillate again based on the 2nd time you knocked it (with the same frequency, but different phase effectively)
if you were to knock it again exactly as it finished its first oscillation however, it would swing further, or oscillate with a greater amplitude. Thats effectively forcing it at its natural frequency - causing resonance.

It'll always oscillate at a certain frequency (its natural frequency), no matter how hard you knock it, as its based on the length of the string (and other factors?) which i suppose basically effect the forces acting on the ball.

So generally you can't really model it mathematically as you cannot determine all of the forces holding the object in place, or it'd just get ridiculously complicated?

just speculation again I'm afraid though - its an interesting question

I can do simple harmonic motion, been doing it for a year :P

All I mean is that why do things have a natural frequency as opposed to how it can be modelled with SHM. I've discussed this with my physics tutor a little, and we were talking about the fact that even chemical bonds have a natural mode of vibration which is used in things like MRI etc. but we never really got to exactly why these frequencies exist the way that they are.

I can do simple harmonic motion, been doing it for a year :P

All I mean is that why do things have a natural frequency as opposed to how it can be modelled with SHM. I've discussed this with my physics tutor a little, and we were talking about the fact that even chemical bonds have a natural mode of vibration which is used in things like MRI etc. but we never really got to exactly why these frequencies exist the way that they are.

So, I get that when an object oscillates due to a driving frequency equal to its natural frequency, it will resonate, but I was wondering why exactly do objects have this natural frequency? Is it a mathematical consequence of some sort?

I know also that a few factors affect it such as length, stiffness etc. but how exactly do they affect it? It just seems a little nonsensical that we can't mathematically determine it as opposed to just experimentally determining it (as far as I know, anyway).

I asked a Professor at my Manchester uni interview day, but he was like a systems Biologist and couldn't really answer me

Physics doesn't really answer "why". It answers "how".
You are asking the wrong question. Ask yourself: what do you actually want to know? What are you expecting from the answer? You can only answer "why" by showing that it depends on something else that you already understand. You can go on asking "why" but eventually you get to the point where the answer is "it just is".

You start with the observation that some things oscillate and then seek to understand this. This is done with the mathematical model called SHM which you have been doing for a year. The model says that if the system has a restoring force that is proportional to the displacement from equilibrium, it will oscillate. This oscillation is SHM. The maths calculates the frequency. The maths tells you why insofar as it predicts the behaviour which is observed and expresses it in quantifiable terms.

The natural frequency is a consequence of the configuration of the system.

Let me turn the tables.
Answer me
when I push an object, why does it accelerate?
I don't want "how", I want "why"?

Let me turn the tables.
Answer me
when I push an object, why does it accelerate?
I don't want "how", I want "why"?

i really don't konow. sorry for my bad english anyway... i try to explain this through the dual nature of matter: de broglie said that when something has a big mass he behaves like a particle but has his hown wavelenght(because it is a wave too). the electron has a small mass and principally behaves like a wave but it is also a particle. and so if the electron that is the main factor of chemical bonds, has specific rates of energy if we want to modify his move, when he interacts with others atoms he will modify his move and all the features of his wave. and in fact if we want to move a specific thing and if we want to mathematically calculate his own natural frequency we should consider the total frequency that the system has beacuse of the interactions of lots of electrons and protons (summing every frequency). in this way we can see the big things like waves that always swings but we cannot see their swinging because our eyes are not able to feel their frequencies. so we can explain all this through the quantum nature of matter i think..

i imagined the hole process and next year i'll start studying physics or cheminstry and i hope i will be able to answer this questions.

I have been thinking the same thing. We just started studying the dual nature of particles in my modern physics class, and just finished covering harmonic oscillators and natural frequencies in my intermediate class, and I was wondering if they are related, which is what brought me to this thread. Of all my research though, so far you are the first person I’ve found to have the same theory. Nowhere is it explained WHY objects have a natural frequency, so all we can do is theorize at the moment. The issue with matter waves is that they’re currently considered not to be actual waves, but rather probabilities of finding a particle at a certain point, so if the waves themselves don’t technically really exist, then they can’t be the cause of natural frequency. I for one think it’s certainly something to look into.

This post is 5 years old. Why’d you reply to it ?

Like I said, I had a theory about natural frequency and matter waves being related and started doing research because nothing yet explains why natural frequency exists, and I came across this thread.