Why this approximation is correct?

• gaus12777
In summary, approximation is necessary in science due to the complexity of natural phenomena. Scientists determine the accuracy of an approximation by comparing it to known data and using statistical analysis. The validity of an approximation is influenced by factors such as the complexity of the system, data quality and quantity, and assumptions made. Scientists justify the use of a specific approximation by providing evidence and reasoning. While an approximation can never be considered 100% correct in science, it can be considered valid and useful if it accurately represents the behavior or patterns of the system being studied.
gaus12777

Could you tell me the reason that if pole is close to the imaginary axis, (1) can be same as (2).

The fact that the roots of (1) are close to the imaginary axis tells you (from the real part of the quadratic equation) that 2ζpωp is small. Ignoring that part of (1) gives (2).

1. Why is approximation necessary in science?

Approximation is necessary in science because many natural phenomena and systems are too complex to be fully understood and measured with precision. Therefore, scientists use approximations to simplify the complexity and make predictions or models that can be tested and verified.

2. How do scientists determine the accuracy of an approximation?

Scientists determine the accuracy of an approximation by comparing it to known data or measurements. They also use statistical analysis and mathematical calculations to evaluate the level of error in the approximation.

3. What factors influence the validity of an approximation?

The validity of an approximation is influenced by several factors, including the complexity of the system being approximated, the quality and quantity of data used, and the assumptions made in the approximation process. It is important for scientists to carefully consider these factors to ensure the accuracy of their approximations.

4. How do scientists justify the use of a specific approximation?

Scientists justify the use of a specific approximation by providing evidence and reasoning behind their choice. This may include citing previous studies or experiments that support the approximation, explaining the limitations and assumptions of the approximation, and demonstrating its accuracy through comparisons to real-world data.

5. Can an approximation ever be considered "correct"?

In science, an approximation can never be considered 100% correct. This is because approximations, by definition, involve simplifications and assumptions that may not fully capture the complexity of a system. However, an approximation can be considered valid and useful if it accurately represents the behavior or patterns of the system being studied.

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