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I think the wave equation for a flexible cable including gravity should look like this

[tex]

\frac{\partial^2}{\partial x^2}f(x,t)-\frac{1}{c^2}\frac{\partial^2}{\partial t^2}f(x,t)=g

[/tex]

It this true? (g is the gravitational constant)

Now if I put the boundary conditions [itex]f(x=0,t)=0 [/itex], [itex]f(x=1,t)=0[/itex] and [itex]f(x,t=0)=0[/itex] a solution to the equation would be [itex]f(x,t)=\frac{g}{2}x(x-1)[/itex]. But this tells me that the cable will follow a parabola under the influence of gravity, which is not true. What is the problem?

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# Wave equation with gravity

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