When a foreign mass collides with a mass attached to a spring and adheres to it, the system behaves as a single larger mass, leading to oscillations. The momentum conservation principle applies, where the initial momentum of the moving mass is equal to the combined momentum after the collision. Following the impact, the spring will oscillate based on the new total mass, resulting in a modified displacement pattern. The oscillation frequency will decrease due to the increased mass, affecting the system's dynamics. Ultimately, the combined mass will oscillate around the equilibrium position of the spring.