The general equation for position of a particle performing SHM is of type
$x=A\sin(\omega t+\delta)$
Let initial position be $\alpha$, therefore
$\alpha=A\sin(\delta)$
Let velocity of particle at $x=\alpha$ be $\beta$
$\beta=A\omega\cos(\delta)$
Now you have two equations and two unknowns. Solve them and you may find $A$ and $\delta$