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The Laplace's equation for a rectangular plate is given by a² u a²u ?x² ?y² + and the boundary conditions are : 0, - u(0,y) = 0, u(1,y) = 0 u(x,0) = 100, u(x, 1) Using u = XY and -2 as a separation constant, differential equations X" + 2X = 0 and Y" - AY = 0. 0 < x < 1, 0

Question

Question The Laplaces equation for a rectangular plate is given by
a² u
a²u
?x²
?y²
+
and the boundary conditions are
: 0,
-
u(0,y) =

By considering all possible cases for ?, solve the differential equations to obtain
the eigenvalue and eigenfunction.
(5 mark Solve the boundary value problem using Fourier series. Complete the
integration to find the Fourier coefficients.
Diberi / Gi (b) Pertimbangkan persamaan gelombang
Consider the one-dimensional wave equation
0² u
0t2
Tuniukkan bahay
dimensi
Show that
d The constant c in the wave equation is given by
?T/P
where p is mass per unit length and T is the magnitude of the tension in ???????

The Laplace's equation for a rectangular plate is given by a² u a²u ?x² ?y² + and the boundary conditions are : 0, - u(0,y) = 0, u(1,y) = 0 u(x,0) = 100, u(x, 1) Using u = XY and -2 as a separation constant, differential equations X" + 2X = 0 and Y" - AY = 0. 0 < x < 1, 0

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