A chain lies in a straight line on a horizontal table with part of it hanging over the edge. The chain is always perpendicular to the edge; it slides without friction and falls straight down. The chain has linear mass density A; its total length is L; and the length hanging down from the table top is r(t). (a) Write the Lagrangian for this system and find the equations of motion. (b) The initial conditions at t = 0 are that the length hanging down is r(0) with 0 < x(0) < L and the chain is not moving. Solve for x(t) for 0

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