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1)

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t)=Asinωt and x2(t)=Asin(ωt+2π3) Adding a third sinusoidal displacement x3(t)=Bsin(ωt+ϕ)  bring the mass to a complete rest. The values of B and ϕ are


A) 2A,3π4

B) A,4π3

C) 3A,5π6

D) A,π3

Answer:

Option B

Explanation:

6122021284_y2.PNG

 Resultant amplitude of x1 and x2  is A at angle (π3) from A1. To make resultant  of x1,x2 and x3  to be zero A3 should be equal to A at angle ϕ=4π3 as shown in figure,

  Correct answer is (b)