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Question:

A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, x1(t)=Asinωt and x2(t)=Asin(ωt+2π/3). Adding a third sinusoidal displacement x3(t)=Bsin(ωt+φ) brings the mass to a complete rest. The values of B and φ are?

√2A, 3π/4

A, π/3

A, 4π/3

√3A, 5π/6

Solution:

x1+x2 = Asinωt + Asin(ωt+2π/3) = Asin(ωt+π/3)
Since, x1+x2+x3=0
x3 = Asin(ωt+4π/3)
So, B=A and φ=4π/3