7) Consider the wave equation: 250 x = Uit on the interval Os xst with U(0,t) =0, U(T.t) = 0 and U(x,0)=f(x). Indicate w

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7 Consider The Wave Equation 250 X Uit On The Interval Os Xst With U 0 T 0 U T T 0 And U X 0 F X Indicate W 1 (25.55 KiB) Viewed 23 times

7) Consider the wave equation: 250 x = Uit on the interval Os xst with U(0,t) =0, U(T.t) = 0 and U(x,0)=f(x). Indicate which of the following are true: a) The solutions are separable and can be written U(x,t) = X(X)T(t) b) If U(x,t) is separable, X(X) has eigenvalues proportional to na c) X(X) has eigenfunctions sin(5nx) d) For a given n Tít) is of the form C1 cos(5nt) +C2sin(5nt) with C1, C2 unknown constants. e) For a given n, T() is of the form C1 cos(5nt) +C2sin(5nt) with C1, C2 unknown constants. These constants can be determined completely by the Fourier series of f(x)