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 values of $B$ and $\phi$ are
IIT 2011, Diffcult
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$x_1+x_2==A \sin \omega t+A \sin \left(\omega t+\frac{2 \pi}{3}\right)$
$=A \sin \left(\omega t+\frac{\pi}{3}\right)$
Since, $x _1+ x _2+ x _3=0$
$x_3=A \sin \left(\omega t+\frac{4 \pi}{3}\right)$
So, $B=A$ and $\phi=\frac{4 \pi}{3}$
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