# Resonance and natural frequency

• Theroen
In summary, the natural frequency of an object is the frequency at which it vibrates without any external forces acting upon it. Adding mass to an object changes its natural frequency, making it more difficult for external forces to resonate the object. This is known as damping a system and can also be achieved by making the object lighter. Resonance occurs when the driving frequency is equal to the natural frequency, causing destructive oscillations.
Theroen

## Homework Statement

Ok, this is not homework, just something that's been bugging me and my tutor is unavailable(as usual) to help me. Why does increasing the mass of a system lower its natural frequency, like adding a concrete block to a washing machine. Come to think of it, I'm not even too sure about what natural frequency is. I know that it's the frequency at which resonance occurs, if the driving frequency is equal to the natural frequency, but what determines the natural frequency? How to obtain it?

## The Attempt at a Solution

I figured out that adding a concrete block is not damping, since it becomes a part of the system in oscillation, and not an external resistive force. Therefore the addition of the block does not damp the oscillation, but it changes the system's natural frequency, but then I come back to the problem of how additional mass affects natural frequency.

Every object has a natural frequency which is the way it vibrates without having any external forces acting upon it. If you apply an external force to this object, it will vibrate, but maybe not at it's natural frequency. However is the driving force is more or less equal to the natural frequency, resonance will occur.

Adding a mass to an object alters it's natural frequency - it shouldn't be hard to see why. In large cases such a bridges, adding blocks to it changes it's natural frequency, so it would be more difficult for wind to resonate it given that wind provides a more or less constant driving force.

This is generally called damping a system. The same effect can also happen by making the system lighter - to the end of disrupting the driving forces ability to resonate the system.

Basically remember these 3 instances:

f >> f0 (minimal movement or a very low frequency induced)
f << f0 (system is moved, but very slowly. It may however gain amplitude or increased frequency over time)
f = f0 (ocsilations become large and destructive, this is resonance)

Where f = natural frequency
f0 = driving frequency/force.

Hello,

Natural frequency is the frequency at which a system will oscillate without any external force or disturbance. It is determined by the properties of the system such as its mass, stiffness, and damping. Adding mass to a system will change its natural frequency because it changes the overall mass of the system. This affects the stiffness of the system and therefore changes its natural frequency.

To calculate the natural frequency of a system, you can use the equation f=1/(2π√(k/m)), where f is the natural frequency, k is the stiffness of the system, and m is the mass. This equation shows that as mass increases, the natural frequency decreases. This is because the stiffness remains constant but the mass increases, resulting in a lower natural frequency.

I hope this helps to clarify your understanding of natural frequency. If you have any further questions, please don't hesitate to reach out to your tutor or another scientist for assistance.

## 1. What is resonance?

Resonance is the phenomenon where an object or system vibrates at its natural frequency when exposed to a periodic force or disturbance.

## 2. What is natural frequency?

Natural frequency is the frequency at which an object or system will naturally vibrate without any external forces acting upon it.

## 3. How does resonance occur?

Resonance occurs when the frequency of an external force matches the natural frequency of an object or system, causing it to vibrate with a larger amplitude.

## 4. What are some examples of resonance in everyday life?

Some examples of resonance in everyday life include the vibrations of a guitar string when plucked, the sound produced by a tuning fork, and the swaying of a bridge when a large number of people walk across it.

## 5. How is resonance used in scientific research or technology?

Resonance is used in various scientific fields and technologies, such as in MRI machines to produce images of the body, in musical instruments to produce specific sounds, and in earthquake-resistant building designs to prevent structural damage during earthquakes.

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