A point mass is subjected to two simultaneous sinusoidal displacement in x -direction, x 1 ( t ) = A sin wt and x 2 ( t ) = A sin ( ω t + 2 π ) . Adding a third sinusoidal displacement x 3 ( t )

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A point mass is subjected to two simultaneous sinusoidal displacement in x -direction, $x_{1} (t) = A sin wt$ and $x_{2} (t) = A sin (ω t + \frac{π}{2})$ . Adding a third sinusoidal displacement $x 3 (t) = B sin (ω t + ϕ)$ brings the mass to a complete rest. The value of $ϕ$ is $n \frac{π}{4}$ . Then $n$ is.

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