The transverse vibrations in the 2D plane describe by the wave equation where u is the wave perturbation, x, y, and t are the horizontal, vertical coordinates, and time, respectively. Consider this equation with the PDE Modeler for 2*2 square membrane (the center at 0,0), which is fixed at the two horizontal sides and is free at the two vertical sides. Select the Generic Scalar line in the Options application mode. For both fixed sides, the Dirichlet, u0, and, for the free sides, the Neumann boundaries, u0=0 are specified. Initial conditions are u0=atan(cos(pi/2*y)) and u0 0=3*sin(pi*y).*exp(

The transverse vibrations in the 2D plane describe by the wave equation where u is the wave perturbation, x, y, and t are the horizontal, vertical coordinates, and time, respectively. Consider this equation with the PDE Modeler for 2*2 square membrane (the center at 0,0), which is fixed at the two horizontal sides and is free at the two vertical sides. Select the Generic Scalar line in the Options application mode. For both fixed sides, the Dirichlet, u0, and, for the free sides, the Neumann boundaries, u0=0 are specified. Initial conditions are u0=atan(cos(pi/2*y)) and u0 0=3*sin(pi*y).*exp(sin(pi/2*x)). Set 31 equally spaced values of the times in range 0 5. Represent the final u-values in the 2D and 3D plots that should show the four contour levels and the summer colormap as well as contain the color bar. Resulting u and triangle p, e, t-values should be exported to the MATLAB workspace; display u at t=0.1 at the orthogonal mesh with the tri2grid command when the x and y coordinates are equal to _1, _2.5, , 1 each.

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