A2 It was shown in lectures that the wave equation 8u 2u t 2 has general...

 

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A2 It was shown in lectures that the wave equation 8²u 2²u Ət² მ2 has general solution = c². 00 u(x, t)=sin n=1 NTI L u(0,t)= 0, u(L, t) = 0, an Cos nact L + b₂ sin nact ²). L Explicitly find the coefficients an and b, for the following initial value problems (a) u(x,0)= x(L-1), (1,0) = 0, (b) u(x,0)=0, (x,0) = x(L-x). du Ət A2 It was shown in lectures that the wave equation 8²u 2²u Ət² მ2 has general solution = c². 00 u(x, t)=sin n=1 NTI L u(0,t)= 0, u(L, t) = 0, an Cos nact L + b₂ sin nact ²). L Explicitly find the coefficients an and b, for the following initial value problems (a) u(x,0)= x(L-1), (1,0) = 0, (b) u(x,0)=0, (x,0) = x(L-x). du Ət