I have to find the solution to this problem:
where f(x,t) is a step function:
I know I have to use the duhamel's principle, but I have problem with the integration of f(x,t).
Can anybody help me please?
Such that with initial conditions
Now by D'lamberts we know that
Now by Duhammel's principle the solution is
Note that the region of integration depends on the x and t varaibles. Also the forcing function is non zero in the rectangle (In red in the diagram). In this diagram the function will be zero in any of the shaded (blue) area's and the wave will travel in the white strips.. I hope this helps.