(Solved): 2.8. Hanging chain (a) A chain with uniform mass density per uni ...

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2.8. Hanging chain $${}^{????}$$ (a) A chain with uniform mass density per unit length hangs between two given points on two walls. Find the general shape of the chain. Aside from an arbitrary additive constant, the function describing the shape should contain one unknown constant. (The shape of a hanging chain is known as a catenary.) The unknown constant in your answer depends on the horizontal distance $$d$$ between the walls, the vertical distance $$?$$ between the support points, and the length $$?$$ of the chain (see Fig. 2.14). Find an equation involving these given quantities that determines the unknown constant.