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 BExplanation: 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)