A body performs S.H.M. under the action of force ' F₁ ' with period ' T₁ ' second. If the force is changed to ' F₂ ' it performs S.H.M with period ' T₂ ' second. If both forces ' F₁ ' and ' F₂ ' act simultaneously in the same direction on the body, the period in second will be

Step-by-step solution

F ₁= K ₁ X and F ₂= K ₂ X When forces act simultaneously aligned & F = ( K ₁+ K ₂ ) x & T ₁=2 m K ₁ and T ₂=2 m K ₂ & ~T ^2=4 ^2 m K ₁+ K ₂ & 1 ~T ^2 = K ₁+ K ₂ 4 ^2 ~m = K ₁ 4 ^2 ~m + K ₂ 4 ^2 ~m = 1 ~T ₁^2 + 1 ~T ₂^2 = T ₁^2+ T ₂^2 ~T ₁^2 ~T ₂^2 & ~T = T ₁ ~T ₂ T ₁^2+ T ₂^2 aligned