Discussion Forum



1)

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 $x_{3}(t)= B \sin (\omega t+\phi)$  bring the mass to a complete rest. The values of B and $\phi$ are


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

B) $A, \frac{4\pi}{3}$

C) $\sqrt{3}A, \frac{5\pi}{6}$

D) $A, \frac{\pi}{3}$

Answer:

Option B

Explanation:

6122021284_y2.PNG

 Resultant amplitude of $x_{1}$ and $x_{2}$  is A at angle $(\frac{\pi}{3})$ from $ A_{1}$. To make resultant  of $x_{1},x_{2}$ and $x_{3}$  to be zero $A_{3}$ should be equal to A at angle $\phi= \frac{4 \pi}{3}$ as shown in figure,

$\therefore$  Correct answer is (b)