# Does Increasing Mass Affect the Natural Frequency of Vibration?

• Deepesh
In summary: Both masses are now moving at the same speed and with the same amplitude.In summary, if you increase the mass of an object, the natural frequency of the object will increase.
Deepesh
TL;DR Summary
This is regarding Stiffness and mass included in Vibrations subject and natural frequency of an object
My query here is,
Suppose there is a 2 kg mass
To oscillate it/vibrate it, it will take some force and it will have some natural frequency
Now I increase the mass to 5 kg
so to vibrate it, won't it take more force and so at the end, won't the natural frequency of the object increase? as its more heavy and requires more force to vibrate it?

Hello Deepesh, !

Deepesh said:
Summary:: This is regarding Stiffness and mass included in Vibrations subject and natural frequency of an object

My query here is,
Suppose there is a 2 kg mass
To oscillate it/vibrate it, it will take some force and it will have some natural frequency
Now I increase the mass to 5 kg
so to vibrate it, won't it take more force and so at the end, won't the natural frequency of the object increase? as its more heavy and requires more force to vibrate it?

Vibrations occur when there is an equilibrium situation and some restoring force that works towards this equilibrium. The simplest way to describe this in physics (mathematics) is $$m\ddot x + kx = 0$$with as solutions ##x = A\sin(\omega t + \phi)##. Substitution shows ##\omega^2 = \displaystyle {k\over m}##. In other words: frequency decreases when only ##m## increases.

And it increases when only ##k## (related to your stiffness) increases.

Lnewqban
If we can keep aside formulae for a second?
If you can explain it to me like what happens there practically?
If mass is increasing, isn't making difficult for the force to move/vibrate that body and thus shifting the natural frequency up?

Correct. Inertia wins.

Now if we come back to simple formula for natural frequency i.e omega= underoot (k/m)

If we increase mass here, the N.F would increase.
Inverse proportion

How does this relate to practically that we just discussed?

Thanks

I don't understand the question

Deepesh said:
Now if we come back to simple formula for natural frequency i.e omega= underoot (k/m)

If we increase mass here, the N.F would increase.
Inverse proportion

How does this relate to practically that we just discussed?

Thanks
If you replace mass2 with mass2 in that equation, being mass2 > mass1, the value of the natural frequency (1/seconds) decreases and the value of the period increases (if keeping amplitude and phase the same).
Period = 2 pi / natural frequency

It is only the Second law of Newton.
Taking a spring-mass harmonic vibration for example:
Let's stop when the both masses (small and big) are located at maximum displacement from the equilibrium position.
Both are being pulled towards that equilibrium position by forces of same magnitude, as both masses are attached to similar springs (k) suffering same deformation (x).
Basically, each mass is "loaded" at maximum acceleration and minimum speed.

Now, what happens when we release both masses at the same time?

Spring1 force = spring 2 force = mass1 * acceleration 1 = mass2 * acceleration 2

Last edited:

## 1. What is mass?

Mass is a measure of the amount of matter in an object. It is a fundamental property of matter and is typically measured in kilograms (kg).

## 2. How does mass affect vibration frequency?

The larger the mass of an object, the lower its vibration frequency. This is because a larger mass requires more energy to vibrate at the same frequency as a smaller mass.

## 3. What is vibration frequency?

Vibration frequency is the number of complete cycles of vibration that occur in one second. It is measured in Hertz (Hz).

## 4. How are mass and vibration frequency related?

Mass and vibration frequency are inversely related. This means that as mass increases, vibration frequency decreases and vice versa.

## 5. How can mass and vibration frequency be measured?

Mass can be measured using a scale or balance, while vibration frequency can be measured using a frequency meter or by counting the number of vibrations in a given time period.

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