A particle executes simple harmonic motion between x = -A and x = +A . If time taken by particle to go from x = 0 to A 2 is 2 s, then time taken by particle in going from x = A 2 to A is

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 go from x = 0 to x = A 2 , let the time taken be t₁ . A 2 = A ( t₁) ( t₁) = 1 2 t₁ = 6 Given t₁ = 2 s, we have (2) = 6 = 12 rad/s For the particle to go from x = 0 to x = A , let the time taken be t₂ . A = A ( t₂) ( t₂) = 1 t₂ = 2 t₂ = 2 = 2 12 = 6 s Time taken to go from x = A 2 to x = A is t₂ - t₁ = 6 - 2 = 4 s. Answer: 4 s