Two simple harmonic motions are given by $$x_1 = a\sin\omega t + a\cos\omega t$$ and $$x_2 = a\sin\omega t + \frac{a}{\sqrt{3}}\cos\omega t$$. The ratio of the amplitudes of the first to the second and the phase difference between them respectively are

A

$$\sqrt{\frac{3}{2}}$$ and $$\frac{\pi}{12}$$

B

$$\frac{\sqrt{3}}{2}$$ and $$\frac{\pi}{12}$$

C

$$\frac{2}{\sqrt{3}}$$ and $$\frac{\pi}{12}$$

D

$$\sqrt{\frac{3}{2}}$$ and $$\frac{\pi}{6}$$