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This is to do with forced longitudinal vibration of a rod (bar).

It's basically a problem to do with the linearised plane wave equation (1d).

The rod is fixed firmly at one end, and excited at the other by a harmonic force.

The wave equation (with constant rho/E instead of 1/c^2) is reduced to the helmholtz equation, which is fine. But the boundary conditions which exist (in this example) are at x=0, u=0 (u=displacement) and at x=L, (AE)*du(x,t)/dx=Fcos(wt)

This leads to the solution of the plane wave equation which is:

u(x,t)=Fsin(ax)cos(wt)/(AEcos(aL))

anyway, there is a time dependence there which I'm not really wanting.

How do I remove this? Basically, i don't know if you noticed but I am lost!

At the end of it all i'm looking for the point mobility.

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# Solving 1d Helmholtz with boundary conditions

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