I've come across the following problem: Two otherwise isolated, equal masses m are at rest and connected by a spring with constant k. An impulse is applied to one of the masses along the direction of the spring connecting them. What happens? Qualitatively, I think that the force will both accelerate the whole system and compress the spring, resulting in translational motion of the whole system and SHM about the centre of mass. The proportion of these two types of motion will depend on k and the time over whoch the force is applied. However, I can't quite put this into mathematics. Given the impulse, m and k, is there a way to calculate the c-of-m speed and the chacteristic properties of the oscillation exactly? Any help woild be much appreciated!