Expanding a small oscillation potential in taylor series

AI Thread Summary
Goldstein's equation 6.3 in the chapter on oscillations involves expanding a potential in the form of a Taylor series, which has led to confusion regarding the coefficients represented by "ni." The discussion highlights a suggestion to provide a screenshot of the equation for clarity, as not many have access to the book. One participant questions the necessity of using a Taylor series for the energy of an oscillating mass, noting that it is already quadratic with respect to displacement in a spring-mass system. The conversation indicates a need for further clarification on the application of the Taylor series in this context. Understanding the derivation and purpose of the series expansion is essential for grasping the underlying concepts of oscillations.
shehry1
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I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.
 
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see http://en.wikipedia.org/wiki/Taylor_series"
 
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shehry1 said:
I was wondering if someone could help me with Goldstein's equation 6.3 (3rd Edition). It is the chapter of oscillations and all that he has done in the equation is to expand it in the form of a Taylor series. I can't seem to get how all those ni's come to get there.
Not many people have this book. Maybe you should take a screen shot and upload it? From what you're saying, I don't see why you would need a Taylor series for the energy of an oscillating mass. It is already quadratic with the displacement (for a spring-mass system at least).
 

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