A particle executes simple harmonic motion represented by...

$x ( t ) = Asin ( \omegat + ϕ )$

$v ( t ) = A\omega cos ( \omegat + ϕ )$

$2 = Asinϕ$ $. . . \left(1\right)$

$2\omega = A\omega cosϕ$ $. . . \left(2\right)$

From $( 1 )$ and $( 2 )$

$tanϕ = 1$

$ϕ = 45 °$

Putting the value of $ϕ$ in equation $( 1 )$

$2 = A\left\{\dfrac{1}{\sqrt{2}}\right\}$

$A = 2\sqrt{2}$

$x = 2$