Does Mass Affect Vibration Response in Single Degree of Freedom Systems?

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In summary, the Time Period of a single degree of freedom system is directly proportional to its mass and stiffness. This means that a system with a larger mass will have a longer Time Period and a greater peak deformation. However, this seems contradictory since a larger mass should offer more inertia and result in less peak deformation. Further clarification is needed.
  • #1
jrm2002
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Considering the free vibration response of a single degree of freedom system:

It is observed ,that, larger the Time Period (Vibration Period -"T") of the system(consider a single degree of freedom system), greater is the peak deformation of the system.Right?

Time Period on the other hand is directly proportional to the mass (m)(T=2*pi*sqrt(m/k)) , k being the stffness of the system.

This means a system having more mass hence more "T" will have higher peak deformation.Right?

But if a system has more mass it offers more inertia, right?Now, if the system offers more inertia should'nt the peak deformation be less??

Plz. help!
 
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  • #2
jrm2002 said:
It is observed ,that, larger the Time Period (Vibration Period -"T") of the system(consider a single degree of freedom system), greater is the peak deformation of the system.Right?
Why do you say that?
 
  • #3


The mass of a single degree of freedom system does affect its vibration response, but it is not the only factor that determines the peak deformation. The time period and stiffness of the system also play a crucial role in determining the vibration response.

As you correctly pointed out, the time period is directly proportional to the mass of the system. This means that as the mass increases, the time period also increases. However, the stiffness of the system also affects the time period. A higher stiffness will result in a shorter time period, regardless of the mass.

In terms of peak deformation, it is true that a system with more mass will have a higher peak deformation than a system with less mass. This is because a higher mass means more inertia, which resists changes in motion and leads to larger deformations. However, as mentioned earlier, the stiffness of the system also plays a role. A stiffer system will have a smaller peak deformation, even if it has a higher mass.

So, in conclusion, while the mass of a single degree of freedom system does affect its vibration response, it is not the only factor. The time period and stiffness of the system also have significant impacts on the vibration response and peak deformation. It is important to consider all these factors when analyzing the vibration response of a system.
 

1. What is free vibration?

Free vibration refers to the motion of a system or object that occurs without any external force or energy being applied. It is a natural response of a system to a disturbance or initial displacement.

2. What factors affect the frequency of free vibration?

The frequency of free vibration is affected by the stiffness, mass, and damping of the system. A stiffer system will have a higher frequency, while a heavier system will have a lower frequency. Damping, which is the dissipation of energy in a system, also affects the frequency of free vibration.

3. How is the natural frequency of a system calculated?

The natural frequency of a system can be calculated using the formula f = 1/2π√(k/m), where f is the natural frequency, k is the stiffness of the system, and m is the mass of the system.

4. What is the difference between free vibration and forced vibration?

Free vibration occurs naturally in a system without any external force being applied, while forced vibration occurs when an external force or energy is continuously applied to the system, causing it to vibrate at a specific frequency.

5. How does damping affect the motion of a system in free vibration?

Damping affects the motion of a system in free vibration by dissipating energy and reducing the amplitude of the vibration over time. A higher damping coefficient will result in a faster decay of the vibration, while a lower damping coefficient will result in a slower decay.

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