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 position of a particle performing an SHM is given by: x = A   sin ( ω t + ϕ ) Since at t = 0   s , the particle is at x = 0 , therefore the initial phase ϕ = 0 . At time t = 2   s , the particle is at x = A 2 . ∴   A 2 = A   sin 2 ω ⇒ ω = π 12   s - 1 Therefore, time period T = 2 π ω = 24   s The total time taken from x = 0 to x = A is T 4 = 6   s . Since the time taken from x = 0 to x = A 2 is 2   s , therefore the