# Calculation of different natural frequencies of a material

1. May 28, 2015

### Akshay Gundeti

Hi,
As far as I know, every material has different sets of natural frequencies associated with it.

For example,
A simple one dimensional oscillator with stiffness "k" and mass "m" has a formula for calculating its natural frequency = 1/2pie*squareroot(k/m). I was wondering if there are different natural frequencies associated with this oscillator then how will we calculate the other frequencies.

Is is just the integer multiple of the above frequency?

Thanks,

2. May 28, 2015

### ash64449

According to me this system has only One natural frequency. Because there is no other value of the frequency that satisfies the equation mω^2=k, since m and k are constants and hence only one ω is possible or one frequency possible.

EDIT: well, there are systems which can vibrate with more that one frequency. For example the standing waves produced in a stretched string. Well, these are obtained by solving equations, the possible frequency it can vibrate. Here by equation,only one frequency is possible.

3. May 29, 2015

### theodoros.mihos

On atomic states, oscillators energy hasn't continues values. Thus, energy interactions limited to these (quantum) amounts of energy.
Because most of local potentials inside atoms likes to harmonic oscillator potential, these energy amounts are like integer products of a basic amount $\hbar\omega$. This is analogue to the static wave conditions for sound waves.

4. May 29, 2015

### nasu

As was mentioned already, the simple harmonic oscillator has only one proper (or "natural") frequency.
More complicated systems have more than one proper frequency. They are also called normal modes frequencies. There are formulas for simple geometric shapes and appropriate boundary conditions. The frequencies may or my not be multiples of a fundamental frequency.
For example, a cord fixed at the ends has frequencies that are multiples of the fundamental. A membrane (like a drum) fixed around the edge does not. The ratios between frequencies are not integer numbers.

5. May 29, 2015

### Akshay Gundeti

Thank you all very much for the explanations. Doubt cleared! :)

I really appreciate them.

Thanks,

6. May 29, 2015

### rumborak

It's probably worth pointing out that usually integer multiples of the natural resonance frequency create resonance too, just to a lesser degree. Those are the harmonics of that frequency (in music called overtones).