Consider the one-dimensional wave equation Ju 1 on the interval [0, 10], subject to the boundary...

 

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Consider the one-dimensional wave equation J²u ə1² on the interval [0, 10], subject to the boundary conditions show that = 100- u(0, t) = 0 and u(10, t) = 0, t > 0. (i) Show that a solution u(x, t) can be written as where the B, and B are constants. [50 marks] (ii) If we also have the initial conditions u(x,0) = ди Ət 2²u əx²¹ u(x, t) =(B₂, cos(nat) + B sin(nat)) sin- n=1 Min 10-z 8 (nn)² 10,5≤x≤ 10 0≤x≤5 (x,0)=0, 0≤x≤ 10. u(x, t) = [₁ sin n=1 пл 2 nax 10 -cos(nat) sin NAI 10 Consider the one-dimensional wave equation J²u ə1² on the interval [0, 10], subject to the boundary conditions show that = 100- u(0, t) = 0 and u(10, t) = 0, t > 0. (i) Show that a solution u(x, t) can be written as where the B, and B are constants. [50 marks] (ii) If we also have the initial conditions u(x,0) = ди Ət 2²u əx²¹ u(x, t) =(B₂, cos(nat) + B sin(nat)) sin- n=1 Min 10-z 8 (nn)² 10,5≤x≤ 10 0≤x≤5 (x,0)=0, 0≤x≤ 10. u(x, t) = [₁ sin n=1 пл 2 nax 10 -cos(nat) sin NAI 10

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Step 12 8u 82u 8x St2 Let by method of separation of variable its solution is ux t Xx Tt Xx X 100 x ... View the full answer