Q: A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x_{1}(t)= A sin ωt and x_{2}(t) = A sin (ωt+2π/3). Adding a third sinusoial displacement x_{3}(t) = B sin (ωt+ φ) brings the mass to a complete rest. The values of B and φ are

(a) $\large \sqrt{2} A , \frac{3 \pi}{4}$

(b) $\large A , \frac{4 \pi}{3}$

(c) $\large \sqrt{3} A , \frac{5 \pi}{6}$

(d) $\large A , \frac{ \pi}{3}$

Ans: (b)