A particle executes simple harmonic motion represented by displacement function as $x ( t ) = A \sin ( \omega t + \phi )$. If the position and velocity of the particle at $t = 0 \mathrm {~s}$ are 2 cm and $2 \omega \mathrm {~cm} \mathrm {~s} ^ { - 1 }$ respectively, then its amplitude is $x \sqrt { 2 } \mathrm {~cm}$ where the value of $x$ is $\_\_\_\_$.