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Q.

A point mass is subjected to two simultaneous sinusoidal displacement in x-direction,x1t=A  sinωt         and        x2t=A  sinωt+2π/3 . Adding a third sinusoidal displacement x3t=B  sinωt+ϕ  brings the mass to a complete rest. The values of   B  and  ϕare 

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a

2A,3π/4

b

A,     4π/3

c

3A,5π/6

d

A,π/3

answer is B.

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Detailed Solution

Given  x1+x2+x3=0x3=x1+x2Bsinωt+ϕ=Asinωt+A  sinωt+2π/3

Using  sinC+sinD=2sinC+D2cosCD2

We get  

B   sinωt+ϕ=2A  sinωt+π/3cosπ/3B  sinωt+ϕ=A  sinωt+π/3B  sinωt+ϕ=A  sinωt+4π/3B=Aϕ=4π/3

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A point mass is subjected to two simultaneous sinusoidal displacement in x-direction,x1t=A  sin ωt         and        x2t=A  sin ωt+2π/3 . Adding a third sinusoidal displacement x3t=B  sin ωt+ϕ  brings the mass to a complete rest. The values of   B  and  ϕare