Question

A particle executes SHM from X equals to -A TO A time taken for it to go from O to A/2 IS

Answer 1

when a particle executes a SHM:
    d^2 x/d x^2 = - ω² x

Time period = T for the particle to go from x = -A to A and then back to -A.
Here A is the amplitude.
     
   x = A sin (ω t)      ,  let Ф = phase initial = 0 without loss of generality.

T = 2π/ω 
         x = 0 when t = 0
         x = A/2  when  sin ωt =1/2  

        =>  t  = π/6ω = T/12

Thus in one by 12th of time period the particle goes from 0 to A/2.