String Under Tension with a transvers force distribution

[ts547]

Homework Statement

A string under tension T is stretched between O and L , and a transverse force
distribution

F(x) = Ax(L-x)

is applied (A a constant). Find the transverse displacement pattern.

Homework Equations

Possibly the wave equation
lots of integrals

The Attempt at a Solution

Not to sure at the moment, having a mental block. A hint would be much appreciated. Trying to link to the wave equation.

 

[ts547]

Oh right, mental block over! I think Mr green has the solution! Thanks for the help :)