Suppose a uniform chain of length L is feet is draped over a metal peg anchored into a wall high above the ground level. Assume that the peg frictionless and the chain weighs ρ lb/ft. Figure (a) illustrates the position of the chain where it hangs in equilibrium; if displaced a little either to the right or the left, the chain would slip off the peg. Suppose the positive direction is taken to be downward and denotes the distance the right end of the chain would fall in time t . The equilibrium position corresponds to In Figure B, the chain is displaced an amount x ₀ feet and is held on the peg until it is released at an initial time that is designated as the motion can be represented by a second order differential equation

(a) Find the general solution of the second order equation.

(b) Find a particular solution that satisfies the initial conditions.