A particle moves with simple harmonic motion in a straight line. In first τ s , after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then :

Step-by-step solution

x = - A cos ω t - A + a = - A cos ω τ ...(i) - A + 3 a = - A cos ω 2 τ ...(ii) ∴    - 1 + a A = - cos ω τ ...(iii) and - 1 + 3 a A = - cos 2 ω τ ...(iv) Adding (iii) and (iv) 2 = 3  cos ω τ - 2  cos 2 ω τ + 1 ∴    2  cos 2 ω τ - 3  cos ω τ + 1 = 0 ∴    cos ω τ = 1 2 ∴        ω τ = π 3