The general solution of Wave Equation
Tags: #physics #general solution #wavesEquation
$$\frac{\partial^2 u(x,t)}{\partial t^2}=\sum_{m=0}^{N}\left(b_m\frac{\partial ^m}{\partial x^m}\right)u(x,t) \\ u(x,t)=\int\limits_{-\infty}^{\infty}\left(a(k){\rm e}^{i(kx-\omega_1(k)t)}+ b(k){\rm e}^{i(kx-\omega_2(k)t)}\right)dk \\ u(x,t)=A{\rm e}^{i(kx-\omega t)} \\ \omega_j=\omega_j(k)$$Latex Code
\frac{\partial^2 u(x,t)}{\partial t^2}=\sum_{m=0}^{N}\left(b_m\frac{\partial ^m}{\partial x^m}\right)u(x,t) \\
u(x,t)=\int\limits_{-\infty}^{\infty}\left(a(k){\rm e}^{i(kx-\omega_1(k)t)}+ b(k){\rm e}^{i(kx-\omega_2(k)t)}\right)dk \\
u(x,t)=A{\rm e}^{i(kx-\omega t)} \\
\omega_j=\omega_j(k)
Have Fun
Let's Vote for the Most Difficult Equation!
Introduction
Equation
Latex Code
\frac{\partial^2 u(x,t)}{\partial t^2}=\sum_{m=0}^{N}\left(b_m\frac{\partial ^m}{\partial x^m}\right)u(x,t) \\
u(x,t)=\int\limits_{-\infty}^{\infty}\left(a(k){\rm e}^{i(kx-\omega_1(k)t)}+ b(k){\rm e}^{i(kx-\omega_2(k)t)}\right)dk \\
u(x,t)=A{\rm e}^{i(kx-\omega t)} \\
\omega_j=\omega_j(k)
Explanation
The general solution of is given by above.
Related Documents
Related Videos
Discussion
Comment to Make Wishes Come True
Leave your wishes (e.g. Passing Exams) in the comments and earn as many upvotes as possible to make your wishes come true
-
Julie WrightFingers crossed for passing this exam!Joshua Moore reply to Julie WrightGooood Luck, Man!2023-07-19 00:00:00.0 -
Vincent AlexanderFocusing all my positive energy on passing this exam.Edna Bates reply to Vincent AlexanderGooood Luck, Man!2023-07-31 00:00:00.0 -
Adam BaileyGetting a pass on this test would be a dream come true.Margaret Thomas reply to Adam BaileyNice~2023-09-03 00:00:00.0
Reply