4. (15 points) A uniform chain hangs over the edge of a table as shown below. You may assume that the chain and table are smooth enough that friction is negligible. The length of the chain is L, and its mass is M. At this instant, one-fourth of the chain is hanging off of the table. The height of the table is greater than the length of the chain. Oooooogo a) Use Newton's Second Law to calculate the acceleration of the system at this instant. Express your answer in terms of the given variables and fundamental constants. b) Let x be the length of chain hanging off of the table. Prove that the acceleration of the chain can always be expressed as a = =x c) Express the result of Part (b) as a differential equation. d) The differential equation can be satisfied by the expression x(t) = " (evil + e (it), where xo represents the amount of chain hanging off the table when it is released. Verify that this equation satisfies the result of Part (c). e) Assume that the chain was held in the position sketched above and then released. Sketch the velocity of the end of the chain as a function of time. f) A student wishes to acquire data to verify the theoretical velocity graph in Part (e). Describe an experiment that could be used to gather this data. Include a brief description of the procedure, a sketch, and the equipment required