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 ((omega t + (2 pi)/(3))`. Adding a third sinusoidal displacement `x _3 (t) = B sin (omega t + phi)` brings the mas to a complete rest. The values of (B) and (phi) are.

Options

A. `sqrt (2 A),(3 pi)/(4)`
B. `A, (4 pi)/(3)`
C. `sqrt (3 A),(5 pi)/(3)`
D. `A, (pi)/(3)`

Answer

B

Explanation

Two sinusoidal displacements have amplitude (A) each, with a phase difference of `2 (pi)/(3)`. It is given that sinusoidal displacement `x_3(t)` brings the mass to a complete rest. This is possible when the amplitude of third is (A) and is having a phase difference of `4 (pi)/(3)` with respevt to `x_1(t)` as shown in the figure.
(##JMA_CHMO_C10_011_S01##).