- #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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SUMMARY
The discussion focuses on identifying non-moving points on a 1-D wave represented by the function u(x,t) = sin(πx)cos(πt) + (1/2)sin(3πx)cos(3πt) + 3sin(7πx)cos(7πt). To find these points, participants derive the condition for zero velocity by setting the time derivative of u(x,t) to zero. The key takeaway is that non-moving points occur where the amplitude is constant over time, leading to the equation -πsin(πx)sin(πt) - (3/2)π(3sin(πx) - 4sin³(πx))(3sin(πt) - 4sin³(πt)) = 0. The discussion emphasizes the need for systematic mathematical approaches rather than graphical approximations.
PREREQUISITES- Understanding of wave equations and their physical implications.
- Familiarity with trigonometric identities and derivatives.
- Proficiency in calculus, particularly in solving differential equations.
- Experience with mathematical software like Maple or Mathematica for polynomial factorization.
- Study the derivation of wave equations in physics, focusing on boundary conditions.
- Learn how to apply trigonometric identities to simplify complex expressions.
- Explore polynomial factorization techniques using software like Maple or Mathematica.
- Investigate the implications of stationary points in wave mechanics and their physical significance.
Students and educators in physics and mathematics, particularly those studying wave mechanics, calculus, and differential equations. This discussion is also beneficial for anyone seeking to deepen their understanding of stationary points in wave functions.