A body executes SHM under the action of force ' F₁ ' with time period ' T ₁ '. If the force is changed to ' F ₂ ', it executes SHM with period ' T ₂ '. If both the forces ' F ₁ ' and ' F ₂ ' act simultaneously in the same direction on the body, its time period is

Step-by-step solution

aligned & F ₁= K ₁ x F ₂= K ₂ X F = ( K ₁+ K . & T ₁=2 m K ₁ ~T ₂=2 m K ₂ & T ₁^2=4 ^2 m K ₁ ~T ₂^2=4 ^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