Q. 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 $\phi$
A) $\sqrt{2}A,\frac{3\pi}{4}$
B) $A,\frac{4\pi}{3}$
C) $\sqrt{3}A,\frac{5\pi}{6}$
D) $A,\frac{\pi}{3}$
Explanation
(b) [image:14_image68.emf]
So $B = A,\ \phi = 240{^\circ} = \frac{4\pi}{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.