A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $$x_1(t) = A \sin \omega t$$ and $$x_2(t) = A \sin\left(\omega t + \frac{2 \pi}{3}\right)$$. Adding a third sinusoidal displacement $$x_3(t) = B \sin(\omega t + \phi)$$ brings the mass to a complete rest. The value of B and $$\phi$$ are

A

$$\sqrt{2}A, \frac{3 \pi}{4}$$

B

$$A, \frac{4 \pi}{3}$$

C

$$\sqrt{3}A, \frac{5 \pi}{6}$$

D

$$A, \frac{\pi}{3}$$