- #31
jianxu
- 91
- 0
yes heh, considering I don't know how to get maple to do anything correctly, what are some alternatives to find the roots? Thanks
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Homework Help Overview
The original poster attempts to find the stationary points on a 1-D wave described by a function u(x,t) that represents the displacement of a string over time. The goal is to identify the values of x in the interval (0, 1) where the wave does not move, meaning u(x,t) remains zero for all t > 0.
Discussion Character
- Exploratory, Assumption checking, Mathematical reasoning
Approaches and Questions Raised
- Participants discuss the interpretation of the wave function and its implications for finding stationary points. The original poster simplifies the problem by evaluating at t=0 and differentiating to find where the velocity is zero. Some participants suggest examining the time derivative of the function to identify conditions for non-moving points.
Discussion Status
There are multiple lines of reasoning being explored, including the use of trigonometric identities to simplify the expressions. Some participants provide guidance on using polynomial forms and factoring techniques, while others express uncertainty about the application of these methods. The discussion remains open with various approaches being considered.
Contextual Notes
Participants note the complexity of the trigonometric terms involved and the challenges of using software tools like Maple for simplification. There is an emphasis on finding systematic solutions rather than relying on graphical approximations.