Let at the instant t=0, the particle is at the mean position.
So, the displacement equation of the particle executing SHM is given by, x=Asin(wt)
Where, A and w are the amplitude of oscillation and the frequency respectively.
Let the time taken by the particle in going from mean position to half maximum displacement be t.
∴ A2=Asin(wt)
⟹sin(wt)=0.5
This gives: wt=π6 ∵(π/6=30o)
∴ 2πTt=π6 ⟹ t=T12