Max Tension of a Chain on Vertical Poles: Find T as a Function of L

[djtsmith007]

A chain is attached to the top of a vertical pole of height H located at x=0. The other end of the chain is attached to another pole of height H at x=a. Find the maximum tension T of the chain as a function of the length of the chain L. Assume that the weight density of the chain is $ (lambda)

 

[tanujkush]

Well, how I would go about it is this:

Take a infinitesimally small portion of the chain say at some x, of length dx and do a free body diagram of this. You should end up with a differential equation which you can then
1. integrate to find out the tension at each point in the chain and thus find the max.
OR
2. Find dT/dx from the equation you found and set it to zero, you'll get some value for the angle. That is your position of max tension.

I haven't solved this yet, but intuition tells me the max tension should be somewhere near the point of application.