A point mass is subjected to two simultaneous sinusoidal displace… - Vidyadip

MCQ

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

A
$\sqrt{2} A, \frac{3 \pi}{4}$
✓
$A, \frac{4 \pi}{3}$
C
$\sqrt{3} A, \frac{5 \pi}{6}$
D
$A, \frac{\pi}{3}$

✓

Answer

Correct option: B.

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

b
$x_1+x_2==A \sin \omega t+A \sin \left(\omega t+\frac{2 \pi}{3}\right)$

$=A \sin \left(\omega t+\frac{\pi}{3}\right)$

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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