Two blocks of mass \(M\) and \(2M\) are connected by a light string and placed on a horizontal, frictionless surface. A time-dependent horizontal force \(F(t)\) is applied to the block of mass \(M\) in a direction away from the other block. The magnitude of the force increases linearly from \(0\) at \(t = 0\) to a maximum value \(F_0\) at \(t = T/2\), and then decreases linearly back to \(0\) at \(t = T\). The system is initially at rest. \n\nWhat is the magnitude of the impulse delivered to the block of mass \(2M\) by the string during the time interval from \(t = 0\) to \(t = T\)?