In the figure, two blocks of masses m and 3m are linked by a light, inextensible rope that passes through an ideal pulley. Block m is tied to a spring with force constant k that joins it to the floor. Initially, the spring is in its equilibrium position and the entire system is at rest. a) Find the maximum distance x that the spring elongates if the system starts from rest.
b) What is the speed of the blocks when they have travelled half that distance?