Velocity Field Between Two Plates

Two infinite parallel plates are separated by a distance h. The space between them is filled with a Newtonian fluid: density (rho), viscosity (mu). The lower plate is fixed, but the upper plate executes a sinusoidal motion. (U=A*sin(omego*t). Calculate the velocity field between the plates, and plot some representative profiles.

coordinates x-dir along plate
y-dir normal to plate.

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