The correct option is A x=Asin(ωt+5π6)
For a particle executing SHM, we can say that,
x=Asin(ωt+ϕ) ......(1)
From the data given in the figure,
At t=0,x=A2⇒A2=Asinϕ
⇒ϕ=π6 or 5π6
Differentiating (1) with respect to time on both sides, we get
v=Aωcos(ωt+ϕ)
Also, from the diagram, we can deduce that the particle is moving towards the negative extreme position.
Thus, at t=0, velocity of the particle is negative.
∴v=Aωcosϕ<0⇒cosϕ<0⇒ϕ=5π6
Subitituting ϕ=5π6 in (1), we get
x=Asin(ωt+5π6)
Thus, option (a) is the correct answer.