Problem S2. Consider a uniform flexible chain of a fixed length L > 0 which hangs between points P = (x1, y1) and Q - (X1, $2). Let y = y(x) be the curve which describes the shape of the chain. Find an equation for the y(x) which minimizes the potential energy of the curve given by I(y) = pgy V1 + (y')?dx, x1 where p is the uniform density of the chain and g is the acceleration due to gravity