A particle executes S.H.M. between x = -A and x = +A . The time taken for it to go from mean position O to A 2 is T₁ and to go from A 2 to A is T₂ , then ( 30^ = 1/2 , 90^ = 1 )

Step-by-step solution

The equation of simple harmonic motion starting from the mean position is given by x = A ( t) . For the particle to travel from the mean position x = 0 to x = A 2 , the time taken is T₁ . A 2 = A ( T₁) ( T₁) = 1 2 T₁ = 6 T₁ = 6 For the particle to travel from the mean position to x = A , the total time taken is T₁ + T₂ . A = A ( (T₁ + T₂)) ( (T₁ + T₂)) = 1 (T₁ + T₂) = 2 T₁ + T₂ = 2 Substituting the value of T₁ : T₂ = 2 - 6 = 3 - 6 = 2 6 = 3 Comparing T₁ and T₂ , we get T₂ = 2T₁ . Therefore, T₁ Answer: T₁ < T₂