QUESTION a) Use the d'Alembert solution method to solve the following wave equa- tion u u...

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QUESTION a) Use the d'Alembert solution method to solve the following wave equa- tion u u -0 <t< x, L >0 subject to initial conditions u(x, 0) = sin 2.r, du (x,0) = e". b) Find the solution of the following wave equation 1Pu 0 < r<T, t> 0, 9 dr subject to the boundary conditious u(0, t) = 0, u(7,t) = 0, t>0, and initial conditions u(r, 0) u:(x, 0) = 1, = T- r, 0 <r<T, 0 <x< T. QUESTION a) Use the d'Alembert solution method to solve the following wave equa- tion u u -0 <t< x, L >0 subject to initial conditions u(x, 0) = sin 2.r, du (x,0) = e". b) Find the solution of the following wave equation 1Pu 0 < r<T, t> 0, 9 dr subject to the boundary conditious u(0, t) = 0, u(7,t) = 0, t>0, and initial conditions u(r, 0) u:(x, 0) = 1, = T- r, 0 <r<T, 0 <x< T.