Question 6 The separated solutions of the 1D wave equation = The possible separated solutions are listed below: 8²u dx²

[answerhappygod]

Question 6 The Separated Solutions Of The 1d Wave Equation The Possible Separated Solutions Are Listed Below 8 U Dx 1 (68.79 KiB) Viewed 45 times

Question 6 The separated solutions of the 1D wave equation = The possible separated solutions are listed below: 8²u dx² terms, 1 d'u 1) X(x) = cos(kx), sin(kx) or a mixture of these terms and T(t) = cos(kct), sin(kct) or a mixture of these terms, ,e- are solutions of the form X(x)T(t). 2) X(x) = = x, 1 or a mixture of these terms and T(t) = t, 1 or a mixture of these terms, 3) X(x) = ekx, -kæ or a mixture of these terms and T(t) = eket, ekct or a mixture of these Suppose that the boundary conditions are are: du(x,t) 𐐀х a) What are the boundary conditions for X(x)? (Explai.. b) Find the separated solutions that can match these boundary conditions. Explain carefully why vou reject some of the solutions (1-3) and how you use the boundary conditions. c) Using (b) construct the general solution for u(x, t). |z=0= 0 and u(2,t) = 0