Two blocks of masses \(m_1\) and \(m_2\) lie on a horizontal, frictionless surface and are connected by a light spring. The system is initially at rest. Starting at time \(t = 0\), a time-dependent horizontal external force \(F(t) = bt\), where \(b\) is a positive constant, acts on mass \(m_1\) to the left. What is the speed of the center of mass of the two-block system at time \(t = T\)?