# On ways of describing the shape of strings fixed at 2 points [duplicate]

I was trying to derive the function $$h(x)$$ that describes the shape of a string fixed at two points with distance $$D$$ (which aligned with the x-axis), in other words, $$h(0)=h(D)=0$$ but I got stuck.

I am interested in a solution that involves Lagrangian mechanics, as I am curious to know how one should solve a problem where the object in question is not rigid with the tool. All I could get is that the integral $$\int_0^D\sqrt{1+h'(x)}\mathrm dx=L,$$ where $$L$$ is the length of the string.

• A Fourier series of sine waves? – Pieter Dec 30 '19 at 20:00
• This might help: math.stackexchange.com/q/2261921. The shape you are describing is called catenary. – Mr. Xcoder Dec 30 '19 at 20:07