- #31
voko
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I do not understand how you get 2pi/ As I said, you should have -9/E in the brackets.
Analyzing the Harmonic Oscillator: Maximal Velocity and Turning Points
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Homework Help Overview
The discussion revolves around a particle subject to specific forces and the analysis of its motion, particularly focusing on maximal velocity, turning points, and harmonic approximation. The subject area includes classical mechanics, specifically the study of harmonic oscillators and potential energy functions.
Discussion Character
- Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking
Approaches and Questions Raised
- Participants explore the relationship between kinetic and potential energy, questioning the conditions under which maximal velocity occurs. They discuss the implications of energy conservation and the characteristics of potential energy functions. Some participants raise questions about the existence of turning points and the nature of oscillations based on energy levels.
Discussion Status
The discussion is active, with participants providing insights and questioning each other's reasoning. Some have offered guidance on sketching force and potential energy graphs to better understand the problem. There is ongoing exploration of the relationship between energy and turning points, with multiple interpretations being considered.
Contextual Notes
Participants note the constraints of the problem, including the requirement to find turning points as a function of energy and the implications of negative energy values. There is also mention of specific assumptions regarding the behavior of potential energy at different values of x.
- #32
CAF123
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voko said:
See my edit before. It's not that I had -9/E which caused me to get 2pi, it was because I said 8 = 2√2!
- #33
voko
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The two values are pretty darn close if you ask me. I am not looking forward to rechecking all the algebra again, anyway :)
- #34
CAF123
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Not to actually proceed with this method, but would it be possible to go ahead and use the taylor approximations (sin2θ ≈ 2θ and cos2θ ≈ 1- (2θ)^2/2) at the integration stage to show that for small oscillations I recover the same results?
- #35
voko
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I guess the most direct way would be to linearize the original integrand. Your method might work, too.
But, in the end of the day, you got an about 1% difference, which I think is very good.
But, in the end of the day, you got an about 1% difference, which I think is very good.
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