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Variable Linear Mass Density

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2. A nonuniform wire of length L and mass M has a variable linear mass density given by mu = kx where x is the distance from one end of the wire and k is a constant.

(a) Show that M = (kL^2)/2.

(b) Show that the time t required for a pulse generated at one end of the wire to travel to the other end is given by t = sqrt(8ML)/9T, where T is the tension in the wire.

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Please see the attached file.

I am using the symbol " m " for linear mass density for the ease of typing
(a)

Here m = k.x
Consider a small length dx of the wire, for this small length the mass is ...

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