Two masses m ₁ and m ₂ connected by a spring of spring constant k rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is-

Step-by-step solution

Let the masses be slightly displaced by x ₁ and x ₂ from this equilibrium position in opposite direction so net stretch in spring is x = x ₁+ x ₂ . Because of this a restoring force kx will act on each mass and therefore equation for m ₁ & ~m ₂ will be m ₁ d ² x ₁ dt ² =- kx and m ₂ d ² x ₂ dt ² =- kx but as x = x ₁+ x ₂ d ² x dt ² = d ² x ₁ dt ² + d ² x ₂ dt ² replacing values of d ² x ₁ dt ² and d ² x ₂ dt ² from acceleration equations we get d ² x ₂ dt ² =- ( 1 ~m ₁ + 1 ~m ₂ ) kx also if 1 ~m ₁ + 1 ~m ₂ = 1 ~m t