Two masses $m_1 = 7 \, kg$ and $m_2 = 6 \, kg$ are attached by a spring and rest on a frictionless table. The masses are at rest and the spring unstretched when a force $F = 78 \, N$ is applied to the second mass.
(a) What is the acceleration of $m_2$ the instant the force is applied, before the spring can stretch?
(b) What is the acceleration of the system's center of mass the instant that the spring reaches its maximum stretch?
(c) What is the speed of the system's center of mass 8 seconds after the force is first applied?