# Deriving the Correction Factor for Non-Ideal Spring Frequency Equation

• amr55533
In summary, the equation ωn=[k/m]^0.5 can be used to calculate the natural frequency of a hanging spring and mass system. However, for a non-ideal spring, a correction factor of ms/3 must be added to the equation. This correction factor can be derived by referring to the link provided.
amr55533

## Homework Statement

In general, I know that you can use the equation ωn=[k/m]^0.5 to calculate the natural frequency of a hanging spring and mass system.

However, for a non-ideal spring (where the mass of the spring isn't negligible) a correction factor is added to the equation and it becomes:

ωn=[k/(m+ms/3)]^0.5

where k is the spring constant, m is the mass of the hanging mass, and ms is the mass of the spring.

How would you derive the ms/3 correction factor in this equation? I'm trying to prove that the equation is viable.

Thanks!

## 1. What is the non-ideal spring frequency equation?

The non-ideal spring frequency equation is a mathematical formula used to calculate the natural frequency of a spring-mass system that takes into account the effects of non-idealities such as mass of the spring, damping, and external forces.

## 2. Why is it important to derive the correction factor for the non-ideal spring frequency equation?

Deriving the correction factor is important because it allows for a more accurate calculation of the natural frequency of the system, taking into account the non-idealities that can affect the behavior of the spring-mass system.

## 3. How is the correction factor for the non-ideal spring frequency equation derived?

The correction factor is derived by analyzing the equations of motion for the spring-mass system and applying mathematical techniques such as Fourier transforms and Laplace transforms to account for the non-idealities in the system.

## 4. Can the correction factor be applied to any non-ideal spring-mass system?

Yes, the correction factor can be applied to any non-ideal spring-mass system as long as the equations of motion for the system are known and the non-idealities can be quantified.

## 5. How does the correction factor affect the natural frequency of a spring-mass system?

The correction factor can either increase or decrease the natural frequency of a spring-mass system, depending on the non-idealities present. In general, the more non-idealities present in the system, the larger the correction factor will be and the more it will affect the natural frequency.

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