# Calculation of different natural frequencies of a material

• Akshay Gundeti
In summary, the conversation discusses the concept of natural frequencies and how they are calculated for different systems, such as a simple one dimensional oscillator. While this oscillator has only one natural frequency, more complex systems may have multiple frequencies, also known as normal modes frequencies. The ratios between these frequencies may or may not be integer numbers. Additionally, it is mentioned that integer multiples of the natural frequency can also create resonance, known as harmonics.
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,

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.

Akshay Gundeti
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.

Akshay Gundeti
Akshay Gundeti said:
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,
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.

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

I really appreciate them.

Thanks,

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).

## 1. How is the natural frequency of a material calculated?

The natural frequency of a material is calculated by using its physical properties such as density, stiffness, and geometry. These values are then used in an equation known as the fundamental frequency equation, which calculates the natural frequency of the material.

## 2. What factors affect the natural frequency of a material?

The natural frequency of a material can be affected by factors such as its physical properties, shape, and boundary conditions. For example, a material with a higher stiffness will have a higher natural frequency, while a material with a larger mass will have a lower natural frequency.

## 3. Can the natural frequency of a material be changed?

Yes, the natural frequency of a material can be changed by altering its physical properties or shape. For example, increasing the stiffness of a material will increase its natural frequency, while changing its shape can also affect its natural frequency.

## 4. How is the natural frequency of a material used in engineering?

The natural frequency of a material is an important factor in engineering design. It is used to determine the stability and performance of structures and components, and can help engineers select the appropriate materials and dimensions for a given application.

## 5. Are there any limitations to calculating the natural frequency of a material?

Yes, there are some limitations to calculating the natural frequency of a material. The equation used to calculate the natural frequency assumes that the material is homogeneous, isotropic, and has a simple geometry. In reality, materials may have variations in their properties and complex shapes, which can affect the accuracy of the calculated natural frequency.

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