A uniform spool of mass M and radius R is set on end on a table at a distance L from the edge and released from rest. A string is wound tightly around the spool. The free end of the string passes over a frictionless and massless pulley and hangs off the edge of the table. An object of mass m is attached to the free end of the string. 1=MR2 a) Construct the Lagrangian of the system. b) Find the equations of motion. c) Determine the time required for the spool to reach the edge of the table.