Two identical blocks on a horizontal frictionless surface are attached to identical ideal springs of spring constant \(k\). Both systems execute simple harmonic motion with period \(T\) and amplitude \(A\) about their respective equilibrium positions at \(x = 0\). The position as a function of time \(t\) for each oscillator is given by
\[ x_1(t) = A \cos\left(\omega t - \dfrac{\pi}{3}\right) \]
\[ x_2(t) = A \cos\left(\omega t + \dfrac{\pi}{6}\right) \]
Which oscillator first achieves its maximum kinetic energy after \(t = 0\), and what is the direction of the velocity of Oscillator 1 at \(t = 0\)?