A particle executes simple harmonic motion between x = - A and x = + A . If it takes a time T 1 to g 0 from x = 0 to x = A / 2 and T 2 to go from x = A / 2 to x = A . Then

Step-by-step solution

Equation of SHM x = a sin ω t at x = 0   ;   t o = 0 at x = A 2 f r o m   e q u a t i o n   A 2 = a sin 2 π T t 1 ⇒ t 1 = T 12 at x = A from equation   A = a sin 2 π T t 1 ⇒ t 1 = T 4 so time from x = 0   t o   x = A 2 T 1 = t 1 - t o = T 12 and time from x = A 2   t o   x = A T 2 = t 2 - t 1 = T 4 - T 12 = T 6 so T 1 < T 2