Two masses m₁ and m₂ are placed on a frictionless horizontal surface and connected by a spring having a spring constant k . The system is released from rest after the spring is initially stretched by a distance x₀ . Determine the respective distances moved by m₁ and m₂ before they come to rest again.

Step-by-step solution

Since no external force acts on the system in the horizontal direction, the center of mass remains at rest. Let d₁ and d₂ be the distances moved by m₁ and m₂ respectively before they come to rest again. From the conservation of the center of mass position: m₁ d₁ = m₂ d₂ The system is released from rest with the spring stretched by x₀ . The masses will come to rest again at the other extreme position of the oscillation, where the spring is compressed by x₀ . The total change in the length of the spring is x₀ - (-x₀)