The angular frequency is $\omega = 2\pi u = 2\pi$ rad/s. Write the motion as $x = A\cos(\omega t + \varphi_0)$, so that $x_0 = A\cos\varphi_0$ and $v_0 = -A\omega\sin\varphi_0$.

Amplitude: squaring and adding,

$$A = \sqrt{x_0^2 + \left(\frac{v_0}{\omega}\right)^2} = \sqrt{3^2 + \left(\frac{6\pi}{2\pi}\right)^2} = \sqrt{9 + 9} = 3\sqrt{2} \approx 4.2 \text{ cm}.$$

Initial phase: $\cos\varphi_0 = \dfrac{x_0}{A} = \dfrac{3}{3\sqrt{2}} = \dfrac{1}{\sqrt{2}}$. Since $v_0 > 0$, $\sin\varphi_0 = -\dfrac{v_0}{A\omega} < 0$, so $\varphi_0$ lies in the fourth quadrant:

$$\varphi_0 = -\frac{\pi}{4}.$$

Equation of motion:

$$x = 3\sqrt{2}\cos\!\left(2\pi t - \frac{\pi}{4}\right) \text{ cm}.$$